U.S. Secretary of State Cyrus Vance today reinforced American support for the Spanish monarch's march toward establishing a parliamentary democracy in a busy 20-hour visit.

Vance met with King Juan Carlos, Premier Adolfo Suarez and Foreign Minister Marcelino Oreja on the bilateral defense treaty, the London NATO Council meeting and the Lodon conference of leaders of the world's industrial nations.

The Secretary, according to U.S. officials, spent much of his time in the talks obtaining "intelligence" on the political situation and on next month's parliamentary elections.

The 6,000 candidates running for 350 Assembly and 207 Senate seats in the June 15 elections represent 18 coalitions and at least 16 parties, including the recently legalized Communist Party.

The visit is bound to bolster the candidacy of Premier Suarez, Sources close to the premier predict that the centrist coalition backing him should win between 40 and 47 per cent of the seats in th lower house.

Vance set the tone of the visit when he arrived from London yesterday afternoon, saying: "We have the greatest admiration for the actions taken under the leadership of the king to strengthen the institution of democracy."

At the request of Spanish officials, the United States played down the idea that Spain's coming free elections, a free Parliament and the pledge of a new constitution have opened the way for Spain's early entry into NATO, but this message was clearly implicit in the visit.

Spain does not want NATO membership to become a major campaign issue, for Communists, Socialists and far-rightists are opposed to joining the aliance. The Suarez administration wants the debate postponed until the issue can be taken up in Parliament, sources said.

Also opposed to NATO entry are some senior military officers, who fear that the relationship will break down the armed forces' devotion to fighting subversion at home.

Vance and Foreignlateral military, economic, cultural and scientific relationships under the provisions of the 15-month-old Spanish-American treaty. They presided at the deliberations of the first session of the joint council.

Vance was joined by Gen. George Brown, chairman of the joint chiefs of staff, who stopped in Madrid today enroute to a NATO meeting in Brussels, plained that the United States hopes that the provision in the treaty for a military council will help to teach the Spanish defense establishment "planning " so it can eventually mesh with NATO. The treaty links Spain to the alliance through the United States.

There appear to be no major issues between the United States and Spain. Differences over the supply of enriched uranium and over licenses for eight nuclear-power reactors, to be built by American companies, have been settled for the time being. The Carter administration has also halted efforts to impose import fariffs on Spanish shoes.

Vance felw to Thran, Iran, this afternoon for a meeting of the Central Treaty Organization.