North Yemeni President Ali Abdullah Salih told Vice President Bush during talks here today that his government is eager to improve relations with the United States, after years of close association with the Soviet Union, according to U.S. officials who attended the meeting.

The North Yemeni request for closer ties with Washington comes after a bloody coup in South Yemen in January that resulted in a takeover by a hard-line, pro-Soviet group. The coup next door has upset the leadership here and raised concern in Washington.

The disclosure of the North Yemeni desire to move away from the Soviet Union is the latest indication that the South Yemeni coup is having wide-reaching repercussions in the region and may end by seriously undermining Soviet influence here.

At a press conference later today in Sanaa, the North Yemeni capital, Bush said that in his talks with Salih and other North Yemeni officials he did not get the feeling that the strong Soviet presence here would continue to block better ties with the United States "on all fronts."

Bush and his aides were clearly pleased by the outcome of the talks with Salih, which the vice president described as "very frank" and "lively." He said that President Reagan had invited Salih to Washington and he announced a $5 million increase in U.S. economic aid to North Yemen.

The United States and the Soviet Union engaged in a sharp competition for influence here starting in the mid-1970s. But, despite a $400 million arms sale by the Carter administration in 1979, the Soviet Union had been winning out, partly because of a waning U.S. interest in the country.

Bush aides had been somewhat apprehensive about the visit here, after learning that pro-Soviet elements in the government were seeking to disrupt it by harassing the visiting U.S. delegation and possibly provoking anti-American demonstrations. But Salih had learned what was being planned and quickly put a stop to it, a Bush aide said.

Even before the coup in South Yemen, the North Yemeni attitude toward the United States had taken a turn for the better with the first discovery of oil in this country by an American firm, Hunt Oil Co. of Dallas.

Bush aides said the vice president had been particularly eager to come here on his eight-day tour of the region to take advantage of the reported new willingness by North Yemen to move closer to the United States.

That desire was almost immediately made clear by the warm reception Bush received. On his arrival yesterday and again today during a visit to Sanaa's old central market, Bush was warmly applauded by crowds lined up in the streets -- the only stop on the trip where this has happened. His visit here, the first by any high-ranking U.S. official since that of Secretary of State William P. Rogers in 1972, is being treated as a major event by the government.

"The finding of oil here has been like a second coming of the Prophet Mohammed," remarked one local U.S. official, who said the Soviets had sought oil here for years but failed to find any.

The discovery promises to make North Yemen, one of the two poorest nations on the Arabian peninsula -- South Yemen is the other -- an oil exporter by 1988. It will provide the country with revenue to add to the $1 billion in remittances from Yemeni workers abroad that now constitutes its main source of income.

Hunt Oil Co., owned by Ray L. Hunt, a friend of the vice president's, has built the country's first oil refinery here in Marib, on the edge of the still-undefined border with Saudi Arabia and the vast desert known as the Empty Quarter.

The 10,000-barrel-a-day refinery, which can supply about 40 percent of this country's needs, will be inaugurated Saturday by Salih and Bush at a ceremony before the vice president returns to Washington.

Last December, Hunt gave up a 49 percent share in the Alif oil field outside Marib to another American oil firm, Exxon. The two are joining forces to build a 250-mile pipeline to the Red Sea to make exports possible. The Alif field has an estimated 400 million barrels of recoverable oil. What the level of North Yemen's exports will be remains unclear, but some estimates run as high as 250,000 barrels a day.