Israeli Prime Minister Shimon Peres yesterday offered to withdraw Israeli troops from the Bekaa Valley region of southeastern Lebanon, where "they are 16 or 17 miles from the doorstep of Damascus," if Syria agrees to placement of a U.N. peace-keeping force in the area.

Peres made the offer at a news conference here after saying earlier in a television interview that his government hopes it will be able to withdraw within nine months the fewer than 10,000 Israeli troops still in southern Lebanon.

The main focus of Peres' White House meeting with President Reagan on Tuesday was to discuss Israel's requests for help in overcoming severe economic problems.

But a priority goal of his three-week-old coalition government is to end the 28-month occupation of Lebanon, which costs the Jewish state $1.2 million a day.

"We have to make a final decision, and this will be done in the coming few weeks, three or four weeks," Peres said Tuesday on ABC's "Nightline" program. "Once our government will decide, the withdrawal will take, in our judgment, between six and nine months."

However, at his news conference yesterday before leaving Washington after three days of talks, Peres made clear that he was not outlining a hard-and-fast timetable for unilateral Israeli withdrawal.

Instead, he indicated that the timing and extent of an Israeli pullback will be influenced by Syria's willingness to provide the security guarantees that Israel says are needed to protect its northern borders from terrorist attacks.

"We are ready to withdraw from the eastern portion of southern Lebanon" even if the move is not accompanied by a simultaneous pullback of Syrian forces, he said.

But, he added, the Israeli troops would have to be replaced by U.N. forces and Syria would have to agree not to move its troops into areas vacated by Israel.

Similarly, Peres continued, withdrawal of Israeli forces from the coastal region to the west would be in conjunction with a continuing role for the Israeli-supported South Lebanon Army, commanded by Christian Gen. Antoine Lahad, to guard against Palestine Liberation Organization guerrillas returning to the area.

Syria and Lebanese Prime Minister Rashid Karami's government, which is under strong Syrian influence, have insisted that Lahad's force must be disbanded.

This disagreement over the status of the South Lebanon Army is the main reason that the United States has held back from acting as mediator in new indirect negotiations between Israel and Syria.

Peres said Israel wants the western region policed by successive zones of authority moving northward into Lebanon from the Israeli border to the Awwali River, where the Israelis are dug in.

He said these zones should be composed of Israeli troops at the border, with the others going to Lahad's force, U.N. forces and the Lebanese army, in that order.

The prime minister refused to elaborate on how far and how fast Israel would go in withdrawing if conditions he described are not met.

He said: "For the time being, I would prefer not to spell out all possibilities because I believe that a low profile and quiet diplomacy are more efficient."

Other Israeli sources said that Peres' Cabinet seems certain to order some unilateral withdrawal, both as a carrot to coax Syria toward cooperation and as a bow to Israeli public opinion.

But, the sources continued, Syrian failure to accommodate some of Israel's security demands would mean some form of continued Israeli presence in Lebanon.

On the economic side, Peres said he was satisfied with his reception here, which included an immediate go-ahead for Israel to begin using $1.2 billion of the $2.6 billion fiscal 1985 foreign aid package being readied for it by Congress.

Reagan also gave Peres a commitment for further economic help, with the size and nature to be recommended by a study group from both countries.

U.S. officials said decisions still were being made yesterday about who will serve on the study group from the American side.

They added that the chairman of the U.S. delegation is likely to be Allen Wallis, under secretary of state for economic affairs.