US Vice-President Mike Pence has told the Egyptian leader the United States would support a two-state solution for Israelis and Palestinians if the two sides agreed to it, seeking to reassure a key Arab ally over President Donald Trump's decision to recognise Jerusalem as Israel's capital.

Mr Pence was in Egypt on the first leg of a three-country tour that includes stops in Jordan and Israel.

It is the highest-level visit by a US official to the region since December, when Mr Trump upended decades of US policy on Jerusalem in a move opposed by Arab leaders including Egypt's President Abdel Fattah al-Sisi.

"We heard President al-Sisi out," Mr Pence told reporters after their meeting, saying the Egyptian leader described his objection to Mr Trump's decision as a "disagreement between friends."

Mr Pence said he assured President Sisi that the United States was committed to preserving the status quo of holy sites in Jerusalem and had come to no final resolution on boundaries for the two parties.

"My perception was that he was encouraged by that message," Mr Pence said.

The Egyptian presidency said in a statement Mr Sisi noted that only negotiations based on a two-state solution could bring an end to the conflict, and that "Egypt would spare no effort to support this."

Mr Pence said he also pressed Mr Sisi about two Americans who have been imprisoned in Egypt since 2013, as well as for reform of Egypt's restrictive laws on non-governmental organisations.

In his meeting with Mr Sisi, the US Vice-President pledged firm US backing in the nation's fight against Islamist militants and said ties between the two countries had never been stronger after a period of "drifting apart."

"We stand shoulder to shoulder with you in Egypt in the fight against terrorism," he said.

Egypt has faced security problems, including attacks by Islamic State militants in the North Sinai region.

Though Mr Pence intends to discuss counterterrorism issues throughout the trip, the Jerusalem decision remains a hot topic.

Mr Trump's announcement, which also set in motion the process of moving the US embassy to Jerusalem from Tel Aviv, prompted Palestinians to reject the United States as a peace broker.

From Cairo, Mr Pence headed to Jordan, where he will meet with King Abdullah, a close US ally.

King Abdullah warned against declaring Jerusalem as Israel's capital, saying it would have a dangerous impact on regional stability and obstruct US efforts to resume peace talks.

Many people in Jordan are descendants of Palestinian refugees whose families left after the creation of Israel in 1948.

Mr Pence will end his trip in Israel, where he will be warmly welcomed following Mr Trump's designation.

He plans to meet Prime Minister Benjamin Netanyahu, address the Israeli legislature and visit the Western Wall.

Mr Pence is not scheduled to meet Palestinian leaders.

They were incensed by Trump's decision on Jerusalem, which upended the longstanding US position that negotiations between Israel and the Palestinians must determine the city's status.

"The United States of America is deeply committed to restarting the peace process in the Middle East," Mr Pence said.

The Trump administration's announcement on Thursday that it was withholding about half the aid it was set to give a United Nations relief agency that serves the Palestinians raised questions about fledgling US efforts to revive peace talks and further undermined Arabs' faith that the United States can act as an impartial arbitrator.