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The Prime Minister is facing demands to say whether Rupert Murdoch asked her to appoint Michael Gove to the Cabinet.
In a letter to Theresa May , deputy Labour leader Tom Watson said it had been "suggested" to him that Mr Murdoch, owner of The Times and The Sun , had lobbied the PM for Mr Gove's return to front-bench politics.
Ms May sacked the now-Environment Secretary last year when he was serving as Justice Secretary, having previously headed the Department for Education.
Mr Watson's letter says: "Given your failure to secure a parliamentary majority and the consequent weakness of your position, it might be tempting to allow yourself to be influenced by powerful media proprietors who can shape the way your government is covered.
"Since you became Prime Minister, has Rupert Murdoch ever made suggestions to you about ministerial or staff appointments?
"Has Rupert Murdoch ever suggested to you that there might be consequences if you fail to take his advice, in terms of his newspapers' coverage of you and your government?"
Downing Street and News UK have been contacted for comment.
After the general election delivered a hung parliament, Mr Watson claimed voters had seen "through the lies of the Murdoch machine who tried to frighten people into voting Tory".
Show all 38 Door of Number 10 Downing Street is seen on the morning after Britain's election in London
REUTERS
Labour leader Jeremy Corbyn leaves his home in north London after he called on the Prime Minister to resign, saying she should "go and make way for a government that is truly representative of this country"
PA
Shadow Chancellor John McDonnell arrives at Labour Headquarters on June 9, 2017 in London, England. After a snap election was called by Prime Minister Theresa May the United Kingdom went to the polls yesterday. The closely fought election has failed to return a clear overall majority winner and a hung parliament has been declared
Getty Images
Caroline Lucas, co-leader of Britain's Green Party, speaks after retaining her seat in the general election, in Brighton
REUTERS
Patrons watch the results for Britain's election in London
REUTERS
Leader of the Liberal democrats Tim Farron celebrates beating Conservative party candidate James Airey (R) following the announcement of the results at the Westmoorland and Lonsdale constituency count at Kendal Leisure Centre on June 9, 2017 in Kendal, United Kingdom. After a snap election was called, the United Kingdom went to the polls yesterday following a closely fought election. The results from across the country are being counted and an overall result is expected in the early hours
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Paul Nuttal, leader of the United Kingdom Independence Party reacts after failing to win the seat of Boston and Skegness at the counting centre for Britain's general election in Boston
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First Minister Nicola Sturgeon arrives at the Emirates Arena in Glasgow, as counting is under way for the General Election.
PA
Anna McMorrin hugs Jo Stevens MP after winning Cardiff North for Labour at the Sport Wales National Centre on June 9, 2017 in Cardiff, United Kingdom. After a snap election was called, the United Kingdom went to the polls yesterday following a closely fought election. The results from across the country are being counted and an overall result is expected in the early hours
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Vince Cable wins the Twickenham election for the Liberal Democrats. Richmond and Twickenham election
Rex Features
Britain's Labour party leader Jeremy Corbyn rubs his face after arriving for the declaration at his constituency in London
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Emily Thornberry speaks after holding her Islington South and Finsbury seat at the Sobell Leisure Centre in Islington, north London
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Britain's Prime Minister Theresa May listens as the declaration at her constituency is made for in the general election in Maidenhead, England, Friday, June 9, 2017. British Prime Minister Theresa May's gamble in calling an early election appeared Friday to have backfired spectacularly, after an exit poll suggested her Conservative Party could lose its majority in Parliament
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Labour Party candidate Emily Thornberry smiles at a counting centre for BritainâÃôs general election in London
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A picture shows the Elizabeth Tower, commonly referred to as Big Ben, and the Houses of Parliament in central London on June 8, 2017, on the night of Britain's general election. Prime Minister Theresa May is poised to win Britain's snap election but lose her parliamentary majority, a shock exit poll suggested on June 8, in what would be a major blow for her leadership as Brexit talks loom
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DUP candidate for Lagan Valley Jeffrey Donaldson celebrates following his election at the Eikon Exhibition Centre in Lisburn as counting is under way for the General Election
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Britain's Home Secretary Amber Rudd attends the count for her seat at a counting centre for Britain's general election in Hastings
REUTERS
Ballots are counted at a counting centre for BritainâÃôs general election in London
Reuters
The London Eye is illuminated in blue, representing the Conservative Party, after the first exit polls announced in Britain's general election
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Election officials count votes in the Emirates Arena in Glasgow, Scotland
EPA
The London Eye is illuminated in red, the color of the Labour Party, after first exit polls of Britain's national election announced in London
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BBC Television centre is illuminated with the exit poll results for Britain’s general election
Eddie Keogh/Reuters
Labour’s Bridget Phillipson (centre) smiles after being announced as the winner of the election for the constituency of Houghton and Sunderland South at a counting centre
Reuters
Members of the election staff prepare to count ballots, in Theresa May’s constituency in Maidenhead
AP
Ballot papers are checked ahead of the count at the Westmoorland and Lonsdale constituency count at Kendal Leisure Centre
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Ballots are counted at a counting centre for Britain’s general election in Kendal
Reuters
Theresa May arrives to vote at a polling station in Maidenhead
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Jeremy Corbyn arrives to cast his ballot at a polling station in north London
EPA
Lib Dems leader Tim Farron outside a polling station at Stonecross Manor Hotel in Kendal, Cumbria
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The leader of the United Kingdom Independence Party (Ukip) Paul Nuttall arrives to vote at a polling station in Congleton
Reuters
Scottish National Party leader Nicola Sturgeon with her husband Peter Murrell (left) the CEO of the SNP after casting their votes at a polling station at Broomhouse Community Hall, Glasgow, Scotland
EPA
Caroline Lucas, co-leader of Britain’s Green Party, arrives with her husband Richard Savage, to vote in Brighton
Reuters
An advertising van showing caricatures of Tim Farron, Theresa May, Jeremy Corbyn and Paul Nuttall with the message who will be looking for a new job as Britain goes to the polls to elect a new government
Rex
Performers pose with puppet caricatures of Britain's Prime Minister Theresa May, leader of the Liberal Democrat Party Tim Farron and leader of the Labour Party Jeremy Corbyn, in front of the Palace of Westminster
Reuters
Dogs wait for their owner outside a polling station in Penally, Wales
Reuters
Police officers speak with a Labour Party activist outside a polling station in London
AP
Benedictine nuns from Tyburn Convent leave after voting in Britain's general election at a polling station in St John's Parish Hall, London
AP
A polling station sign is seen on a telephone box outside the polling station at Rotherwick Hall, west of London
Getty
Both The Times and The Sun endorsed the Conservative Party ahead of the election, with the latter publishing a controversial front page that was highly critical of Labour leader Jeremy Corbyn on the day of the vote.
Last week's general election was the first in which The Sun endorsed a candidate who did not go on to secure a majority, in a development many have suggested reflects the waning influence of the right-wing tabloid press.
David Davis: Speculation over Conservative party leadership is the 'height of self-indulgence'
Following his departure as Justice Secretary Mr Gove returned to work at The Times as a columnist. He secured the UK press' first interview with President Donald Trump.
Mr Murdoch also owns Fox News , the conservative-leaning US TV channel.
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