The Turkish president has accused the United States of stoking violence in the Middle East with its embassy move.
In her remarks, Ms May reiterated her call for an independent and transparent inquiry into the killing of at least 60 Palestinians by Israeli forces in Gaza, saying the “use of live fire and the resulting loss of life is deeply troubling”.
During their joint appearance the Turkish president said he would never accept the embassy move, claiming the US had contributed to the conflict.
“The US claims to be powerful. You are powerful, but you are not right. History will not forgive you. This is the fact that we will observe in the future,” he added.
“Israel will not be forgiven. That’s what we are going to witness in the future too. It all boils down to the fact of making a choice – are we going to side with the strong or side with those who are right?”
President Erdogan added that the Israeli ambassador to Ankara had been expelled on Tuesday afternoon and its own ambassador to Tel Aviv has been recalled for instructions from the government.
While Ms May urged Israel to “show restraint”, she stopped short of blaming Mr Trump’s embassy decision as directly contributing to the bloodshed in the last 24 hours.
“Palestinians have the right to protest, but these protests must be peaceful. We are concerned that extremist elements are seeking to hijack legitimate protests to further their own objectives,” she added.
Their comments came after Ms May had shook hands and posed for photographs with Mr Erdogan outside Number 10 as protestors demonstrating against human rights abuses in Turkey could be heard shouting “Turkish state, fascist state” and waved placards on Whitehall.
Pro-Kurdish groups raised concerns about human rights abuses by Mr Erdogan’s government and urged Ms May to distance herself from the Turkish leader, who has been accused of purging opponents, sacking thousands of officials and jailing critics and journalists.
But during their joint appearance, the Turkish president denied reports that over 200 journalists are currently detained in the country following the failed coup against his administration in 2016.
“You have to make a distinction between terrorists and journalists,” he said. “We are talking about ... Those who have been caught red-handed bearing weapons, those who have been killing people.
“Are we supposed to call them journalists just because they bear the credentials and identity cards? They are not fit to do anything they want to do under the sun, are they?
“Currently, the Turkish judiciary is prosecuting and sentencing individuals who have been associated with terrorism and involved in terrorist actions.”
At the press conference Ms May said she had raised human rights issues with Mr Erdogan, adding: “It is right that those who sought to overthrow the democratically elected government are brought to justice but it is also important that in the defence of democracy, which has been facing extraordinary pressures from the failed coup, instability across the border from Syria and from Kurdish terrorism, Turkey does not lose sight of the values it is seeking to defend.
“That is why today I have underlined to President Erdogan that we want to see democratic values and international human rights obligations upheld.”
She also said the UK would “remain a true friend to Turkey”.
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