Obama said the incident was a "tragedy", but repeated the line of his administration that it was too early to rush to judgement, saying "it's important that we get all the facts".
Obama also said he believed "significant progress" was possible in the Middle East peace process this year, and vowed the "full weight" of US involvement.
$240m investment in a mortgage finance programme in the West Bank, designed to increase homeownership.
$75m to support the Palestinian Authority’s work to improve infrastructure throughout the West Bank and Gaza.
$40m to support Unrwa's Emergency Appeal for Gaza and the West Bank, to improve educational and health services, increase job creation, and repair shelters in Gaza.
$10m to enhance the Palestinian private sector’s competitiveness.
Now is the time to move forward from the current "dead end", he said.
"Not only is the status quo with respect to Gaza unsustainable, but the status quo with the respect to the Middle East is unsustainable, it is time for us to go ahead, move forward on a two-state solution."
Abbas repeated his calls for Israel to lift its blockade of Gaza in the meeting, and described Obama's promise of aid as a "positive sign".
Michael Oren, Israel's ambassador to the US, responded that his country was open to suggestions that would address the needs of the Palestinian people along with Israel's security requirements.
However, Oren defended the blockade as "essential for not only Israel's security, Egypt's security, but it's essential for the peace process".
Israel put the Gaza Strip under siege in 2007, after Hamas seized power of the territory, saying the blockade is needed to prevent weapons smuggling.
The siege allows Israel to control the flow of goods and people going into the Strip.
Ahmed Youssef, an adviser to Ismail Haniyeh, the Hamas leader in Gaza, described Obama's comments as a "step in the right direction".
"If Mr Obama believes that the situation here [in Gaza] is unacceptable it's up to him to change things by asking the Israelis to lift the siege," he told Al Jazeera.
"We' don't only need free flow of goods and building materials. The people of Gaza also need to be given the freedom to travel.
"At present the sick are dying because they cannot go abroad to get the necessary treatment and doctors."
In recent years, US aid to the Palestinians has been sent mostly to the West Bank, governed by Abbas' Fatah movement, or funnelled to Gaza through international agencies.
Washington pledged $900m for the Palestinians at a donors conference in 2009.
Al Jazeera's Patty Culhane, reporting from Washington, said she had been chasing officials to find out how much of that money had actually been paid out.
"The state department said yesterday that in the last year, for Gaza and the West Bank, the US committed to spending $200m," she said.
"I was pushing at the White House trying to figure out where the difference is, where did the money go, and they're basically trying to brush off the question."