The Israeli government, in a direct challenge to President Reagan's Middle East peace initiative, approved three new Jewish settlements in the West Bank today as Prime Minister Menachem Begin vowed in a letter to Reagan that the occupied territory will never again be a part of Jordan.

A ministerial committee with final authority over new settlements announced that two new communities will be established in the Hebron area and a third in "north Samaria," the northern part of the West Bank.

Meanwhile, Israeli authorities announced that eight Israeli soldiers were captured yesterday in Syrian-controlled eastern Lebanon, and a report from Damascus said three Israeli soldiers were killed in a skirmish in eastern Lebanon. The Israeli military command said it had no information on the reported deaths, and it was not clear whether there was a connection between the two reports. Story on Page A25.

Israeli officials denied there was any connection between today's action and Reagan's proposals of last week, which called for a freeze on new and existing settlements while efforts are made to revive the Camp David autonomy talks. But the committee acted less than a week after Reagan's suggestions were presented to Begin and with the full backing of the Israeli government, which last Thursday unanimously and totally rejected the American initiative.

The committee also gave official government blessing to an existing settlement in the occupied Gaza Strip and approved an overall "development program" for the Hebron region without specifying how many additional settlements are foreseen in the plan.

Underscoring the actions, the government tonight made public a strongly worded letter from Begin to Reagan declaring that "the government of Israel will stand by its decision with total dedication."

Employing the Biblical names for the West Bank, the prime minister said, "Judea and Samaria will never again be the 'West Bank' of the Hashemite Kingdom of Jordan, which was created by British colonialism."

The letter, combined with the settlements committee's action, amounted to a direct rebuff of the Reagan initiative and the strongest challenge to date that the administration has faced from Israel.

In another development, the Israeli Cabinet began what was described as its "concluding discussion" of the war in Lebanon, which Begin called "an illustrious, historical campaign" that had ended in "total victory for Israel."

The government press office, quoting "Cabinet sources," said the Begin government believes that "Syrian withdrawal from Lebanon can be achieved peacefully" and that there is "no talk now of military steps to that end." The report said the Cabinet assessment was based in part on beliefs expressed by U.S. Defense Secretary Caspar W. Weinberger, who met with senior Israeli officials here last week.

Today's developments went beyond last week's formal Cabinet rejection of the Reagan initiative. Although Israeli officials insisted that the settlements approved today had long been planned, the action represented the first concrete steps beyond words that Israel has taken to demonstrate that it will not consider the president's proposals.

There are now about 100 settlements in the West Bank with a population of about 30,000 Jewish settlers among 800,000 Palestinian Arabs. Since it came to power in 1977, the Begin government has pursued an aggressive policy aimed at absorbing the territory that Israel captured from Jordan in the 1967 Arab-Israeli war.

In a letter to Begin and a nationally televised speech last week, Reagan called for "the immediate adoption of a settlement freeze by Israel," which he said "more than any other action could create the confidence needed for wider participation" in the long-stalled autonomy talks.

The Camp David peace accords call for an interim, five-year period of autonomy for the Palestinian inhabitants of the West Bank and Gaza during which the final status of the territories is to be negotiated. The autonomy talks among Israel, Egypt and the United States have gone on intermittently for three years with virtually no results.

In an effort to revive the talks and encourage Jordanian participation in them, Reagan also announced last week that the United States favors the eventual "linking" of the territories to Jordan, an idea that is anathema to the Begin government.

In his reply, addressed to "Dear Ron," Begin gave the most complete accounting to date of Israeli and Syrian losses during the war in Lebanon. He said Israel suffered 340 soldiers killed and another 2,200 wounded. The letter said Israel destroyed 405 Syrian tanks (including nine T72s, the most modern tank in the Soviet Union's arsenal), downed 102 Soviet-made planes and took out 21 Soviet-supplied SA6, SA8 and SA9 ground-to-air missile batteries.