The Prime Minister showed his support for the Labour candidate, Bill Tynan, as part of a series of engagements in Scotland before heading to Balmoral to spend the weekend with the Royal Family.
Mr Blair held a round-table discussion with local people in the Hillhouse area of Hamilton, where a controversial children's curfew has been tested.
Accompanied by John Reid, the Secretary of State for Scotland, he talked with residents about the issues facing the area, including crime and keeping young people out of trouble. He expressed interest in the citizens' jury scheme, which had suggested the curfew. He asked how the scheme, which has been extended to cover the whole constituency, operates and how citizens' juries are selected.
The Scottish Parliament may extend citizens' juries to other areas, and the Government has also expressed interest south of the border.
Earlier, the Prime Minister met leading business figures at Bute House in Edinburgh, the official residence of Donald Dewar, the First Minister. Later, Mr Dewar's spokesman, David Whitton, said the Prime Minister and First Minister had also discussed the Scottish executive's legislative programme and events of the past few weeks during a 45-minute meeting, their first since July.
Mr Whitton said: "The Prime Minister is naturally interested, he is keen to see devolution working as much as the First Minister. They had a useful discussion about the various Bills going forward and some of the matters discussed in our Cabinet."
Speaking at a news conference, the Scottish National Party leader, Alex Salmond, said: "Tony Blair's visit to Hamilton shows that Labour have got a definite dose of the jitters at this early state of the campaign. First, Labour broke the convention of not having by-elections during party conferences, and now they have broken the convention that Prime Ministers don't normally campaign in by-elections."
The by-election, on 23 September during the SNP conference, is caused by the elevation to the Lords of George Robertson, the Secretary of State for Defence.Reuse content