His visit will precede a trip by Bush to the Middle East where he would meet Israeli Prime Minister Ehud Olmert and Abbas.
“Bush invited President Abbas to visit Washington on April 24 to discuss the peace talks with Israel and ways to advance those talks,” a senior Abbas aide told Reuters.
U.S. officials said they were checking the report.
At Annapolis in November last year, Bush launched Israeli-Palestinian peace talks on sensitive final status issues such as Jerusalem, the fate of refugees, Jewish settlements and borders.
Bush made his first presidential visit to Israel and the West Bank in January and is expected to make another trip in May.
Abbas told reporters on Wednesday that talks between chief Palestinian negotiator Amed Qurie and Israeli Foreign Minister Tzipi Livni tackled “all the core issues without exception: Jerusalem, refugees, settlements, borders, and security.”
“We hope to achieve a settlement in 2008, there are many obstacles but we hope they will be removed. We are all pressing to reach a settlement by the target date,” Abbas said.
He said Jewish settlement building in and around Jerusalem,political strategy, Israeli army checkpoints and raids were blocking progress towards achieving a deal by the end of this year, a target date set by Bush at Annapolis.
Washington has appointed three U.S. Generals to help the two sides narrow the gaps, monitor implementation of a U.S.-sponsored road map for peace and help draft a security plan between Israel and the future Palestinian state.
Palestinian officials and Western diplomats said U.S. Secretary of State Condoleezza Rice would visit the region later this month for peace talks with Abbas and Olmert.
She would press for the implementation of the road map which calls on Israel to halt settlement construction and on the Palestinians to rein in militants.
“Rice will meet Abbas in Amman on March 30 after the Arab summit in Damascus ends. She will then travel to Israel for talks with Olmert and return to Amman for further talks with President Abbas,” a senior Abbas official said.
“President Abbas will also visit Moscow on April 20 just before his Washington trip to discuss holding an Annapolis follow-up conference in Moscow in mid-June to push for further progress in Israeli-Palestinian talks,” the official said.