Trump made the commitment when he met in New York with Israeli Prime Minister Benjamin Netanyahu, who is in the city to take part in the United Nations General Assembly, which began last Tuesday, EFE news reported.
A statement issued by the Trump campaign's press office said that the GOP candidate "acknowledged that Jerusalem has been the eternal capital of the Jewish People for over 3,000 years.
The United States "under a Trump administration, will finally accept the long-standing Congressional mandate to recognise Jerusalem as the undivided capital of the State of Israel," the statement read.
The US government does not recognise Jerusalem as Israel's capital, like most nations around the world, due to the disputes that exist between Palestinians and Israelis regarding the city and, like many countries, Washington maintains its embassy in Tel Aviv.
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The US Congress has come out in favour of acknowledging Jerusalem as the capital of the Jewish state, but in June 2015 the US Supreme Court backed the contrary position of the Barack Obama administration, EFE news added.
That divergence in stances between the branches of government would end under a Trump administration, the magnate told Netanyahu during their private meeting lasting more than an hour at Trump Tower on Sunday.
The pair "discussed at length Israel's successful experience with a security fence that helped secure its borders", along with US military aid to Israel, regional stability, technology and the Iran nuclear deal, which both men oppose.
Trump said "peace will only come when the Palestinians renounce hatred and violence and accept Israel as a Jewish State", the campaign said in its statement.
The Palestinians claim all of East Jerusalem as their territory, intending to establish the capital of a future state there, but the Israeli government refuses to cede any of the eastern portions of the city it annexed after the 1967 Six-Day War.
While in New York, Netanyahu is also scheduled to meet with Democratic presidential nominee Hillary Clinton.