More than five times as many Jews live in the occupied West Bank now than when Prime Minister Menachem Begin took office in 1977 and the figure can be vastly increased before the end of Begin's term next fall, the government reported today.

In a memorandum widely interpreted here as the opening salvo of Begin's reelection campaign, Mattiyahu Shmuelevitz, director general of the prime minister's office, said 17,400 Jewish settlers live in the West Bank, compared to 3,200 when Begin's Likud coalition took power.

In 1977, Shmuelevitz said, there were 24 West Bank settlements, compared to 68 today. The government, as a matter of policy, does not count satellite settlements of major outposts in the occupied territories in the total. As a result, independent estimates of the number of Israeli settlements usually are higher than the government's.

Shmuelevitz, in a memo to Begin, said the population of West Bank settlements could reach 28,000 by the end of the Likud government's term of office next November. The growth, he added, depends only on "the rate of construction, the planning and the amount of resources allocated toward this end."

Shmuelevitz reported that during the last three years, industrial plants covering 86,000 square yards have been built in the West Bank and that 1,200 industrial workers are employed, 60 percent of them Jewish and the rest Arab. Additionally, 50 more factories are under construction, he said.

Most of the statistics released by Begin's officer were not new. Political observers thus interpreted the prime minister's statements as an attempt to attract hard-line voter support for his reelection bid.