WASHINGTON (Reuters) - The United States will push hard for Palestinian statehood despite a new rightist government in Israel but anticipates a rough road ahead, a U.S. official said on Thursday.

“We’re going to be working hard to see what we can do to move the process forward. But we’re under no illusions. It’s not going to be easy,” said State Department spokesman Robert Wood.

“We have to engage constantly and remind the parties of their obligations and to try to set up a framework, a process for getting us toward that goal of a two-state solution,” Wood added, referring to the goal of separate Israeli and Palestinian states, living side by side in peace.

Israel’s new foreign minister angered Palestinians and raised the prospect of tension with Washington on Wednesday by saying Israel was not bound by a deal to start negotiations on establishing a Palestinian state.

On his first day at the Foreign Ministry, ultranationalist Avigdor Lieberman said the U.S.-backed Annapolis declaration of 2007 “has no validity,” confirming a shift in stance under new Prime Minister Benjamin Netanyahu.

U.S. Secretary of State Hillary Clinton made her first contact with Lieberman on Wednesday, telephoning him from London where she is with President Barack Obama.

“It was primarily to congratulate him on coming into his new position, but no dates have been set for any type of meeting,” said Wood.

Wood said U.S. special envoy to the Middle East, former Sen. George Mitchell, is set go to the region soon.

He did not comment on whether Clinton had raised U.S. concerns over Lieberman’s comments, but said the new Israeli foreign minister was “well aware” of the U.S. position.

“We’re going to pursue that two-state solution, because we believe it’s in the best interests of all the parties in the region,” said Wood.

Lieberman’s anti-Arab rhetoric has particularly alarmed Palestinians as well as Arab leaders in the region. Lieberman says land where many of Israel’s 1.5 million Arabs live should be “swapped” for West Bank Jewish settlements in a peace deal with the Palestinians.

Netanyahu was prime minister from 1997 to 1999 and clashed constantly with the administration of Clinton’s husband, former President Bill Clinton.

Netanyahu is expected to visit Washington soon, possibly as early as next month, an Israeli official told Reuters. However, he said no date had been set yet for that visit.