In the first meeting between the US president and the Israeli prime minister, Trump appeared to tone down commitment to a policy that assures the Palestinians of an independent state.
What is the two-state solution?
In very simple terms, it is a proposed peace deal to end the decades of conflict between the Israelis and the Palestinians.
It calls for independent Palestinian and Israeli states existing side by side. This means creating a Palestinian state on the rough basis of the situation before 1967, when Israel occupied east Jerusalem and the West Bank in a war with its Arab neighbours.
The two-state solution has been endorsed by the United Nations, the European Union, the US, and both the Israelis and the Palestinians.
The UN partition plan from 1947 also proposed two states with Jerusalem placed under separate international control. Jerusalem is considered a holy city by Judaism, Christianity and Islam.
The two-state solution has been backed by successive US governments and endorsed at several international conferences but talks between the parties have always broken down.
Former US President Barack Obama repeatedly emphasised the need for a two-state solution.
What did Donald Trump say?
"So I'm looking at two-state and one-state, and I like the one that both parties like. I'm very happy with the one that both parties like. I can live with either one."
"I thought for a while the two-state looked like it may be the easier of the two, but honestly, if Bibi [Netanyahu] and if the Palestinians -- if Israel and the Palestinians are happy, I'm happy with the one they like the best."
Trump also brought up the issue of moving the US Embassy to Jerusalem, a subject which has angered the Palestinians in the past.
What did Benjamin Netanyahu say?
"There are two prerequisites for peace. First the Palestinians must recognize the Jewish state … Second, in any peace agreement, Israel must retain the overriding security control over the entire area west of the Jordan River."
"Rather than deal with labels, I want to deal with substance," Netanyahu said.
The Israeli Prime Minister did not answer questions about the two-state solution directly.
What was the reaction to the comments?
Palestinian President, Mahmud Abbas, said his government was "ready to deal positively" with the White House, highlighting Trump's appeal to Netanyahu to "hold back" on settlements on occupied Palestinian territory.
Abbas' special advisor said that while a two-state solution was still preferred, his administration was willing to discuss all options, provided Palestinian rights were protected.
Israel's Education Minister, Naftali Bennett, said Trump's comments were the "start of a new era".
"A new era. New ideas. No need for 3rd Palestinian state beyond Jordan & Gaza. Big day for Israelis & reasonable Arabs. Congrats," Bennett tweeted.
The UN Secretary General Antonio Guterres emphasised that the only way to achieve peace between Israel and Palestine was the two-state solution and that everything must be done to preserve that possibility.
He said there was "no Plan B."
The chief of the Arab League, an organisation of Arab countries, said the conflict "requires a comprehensive and just peace based on a two-state solution with an independent Palestinian state."
France, which recently hosted a Israel-Palestine peace summit, also weighed in.
The French Ambassador to UN, Francois Delattre, said "our commitment to the two-state solution is stronger than ever".