A human chain of placard-carrying demonstrators, strung out nearly 15 miles on the road through the Jerusalem hills leading to the capital, demanded "peace now" as they protested yesterday against the policies of Prime Minister Menachem Begin and his government.

They brought signed postcards, perhaps as many as 60,000, to the prime minister's office here - all of them urging more Israeli concessions in the cause of peace.

What started last month with a letter to Begin from 300 young Israeli reserve officers, urging concessions in order to achieve a Middle East settlement, has now grown into what has all the marking of a national peace protest movement. It is too early, however, to calculate what effect, if any, the movement will have on Begin's foreign policies.

The original 300 who collected 60,000 signatures to support their "peace now" demands have now been joined by 350 professors and academicians who recently issued a manifesto in support of the movement. The 350 include some of the most illustrious names in Israeli intellectual life.

In addition, about300 orthodox Jews, including many prominent rabbis, have also signed a petition in support of the movement, saying that "loyalty to the holiness of the land of Israel does not contradict our aspirations for peace with the Arabs in the basis of a fair compromise. The extremist voice beard in our midst does not reflect the view of many of those loyal to the Torah of Israel." The "extremist element" referred to the Gush Emunim, a nationalist group dedicated to settling in the occupied West Bank and which, is pushing for Israeli annexation of territory occupied in the 1967 war.

Earlier this month the "peace now" rally in Tel Aviv attracted a crowd estimated at between 20,000 and 30,000. A rival rally organized by the ruling Likud Party as "Movement For a Secure Peace," attracted about the same number, but the "peace now" movement saw this as a victory.

If the government could not organize a bigger rally, said David Zucker, one of the "peace now" founders," then it proves that Begin does not have the concensus he claims for his policies.'

The original letter to Begin declaed that "A government which prefers the entire land of Israel (meaning the occupied West Bank and Gaza) to a peaceful existence arising from good neighborly relations causes us deep concern . . .

"We are fully aware of the security needs of the state of Israel and the obstacles in the path towards peace, but we know that true security can be achieved only with the advent of peace . . .," the letter asserted.

At first the government an dthe rightist press denounced the 300 peace activists as defeatists, leftists, eltists and the tools of the opposition, although Zucker, in an interview, said he saw the movement as spanning the center of the political spectrum and appealing to people not only in opposition but within the government coalition.

After dismissing the movement out of hand - Finance Minister Simcha Ehrlich said that a movement started by reserve officers "smells of a putsch" - government leaders have now been forced to take notice.

Deputy Prime Minister Yigael Yadin criticized the prostesters for using their military status for making political points - a critism which even their supporters have made - but after meeting with them he asked them to clarify their position and said if it were in accord with his own he would not hesitate to back them publicly. Yadin and his Democratic Movement for Change favor territorial concessions on the West Bank.

Now that the movement has been joined by professors, orthodox Jews and many ordinary people, its image as a creature exclusively of reserve officers has softened. But there are still changes that the movement is made of the country's upper and middle class intellectual elite - not the blue collar voters who put Begin in power. To this charge the "peace now" leaders say that it is always the elite that starts any kind of movement, but that others are joining.

Perhaps the most remarkable convert to the cause is Yeoshafat Harkabi, director of military intelligence when Yitzhak Rabin was prime minister and perhaps the country's leading expert on the Arab world and the Palestinian problem in particular. Harkabi had never been a dove, and has long held that the Arabs are psychologicaly incapable, for the time being at least, of accepting Israel in their midst.

Yet, he joined the 350 academicians who signed the petition, telling Israeli Radio that "Israel's strength is partially borrowed," and that to keep israel strong it was necessary to keep the "credit line" open to the United States. The choice was not devoid of difficulties, he said, but on balance he thought it necessary for the Begin government to show more compromise.