The Teamsters union opened negotiations for a new national freight contract with the trucking industry yesterday after first personally promising President Reagan it would be "reasonable" in its bargaining demands.

"We assured the president that in our . . . negotiations . . . for the National Master Freight Agreement, affecting some 300,000 Teamsters, that we will be as reasonable as conditions permit us to be," Teamsters General President Roy Williams said yesterday after he and 20 other members of the union's executive board met with Reagan at the White House.

The basic motive behind the 30-minute meeting, called by the administration, was political. Reagan says he wants to improve communications with organized labor--to strengthen ties with the few unions he has befriended, such as the Teamsters, and to end warfare with the rest of organized labor, mostly represented by the AFL-CIO.

The administration held several meetings with labor leaders this week. And President Reagan will meet today with AFL-CIO President Lane Kirkland and members of the federation's executive council in an effort, as one White House source put it, to "emphasize his desire to communicate with them."

But administration sources also said Reagan is concerned about the possible inflationary effect of any wage settlements coming in 1982, the heaviest bargaining year in the three-year cycle of labor negotiations. The Teamsters talks are important because they will affect overall costs in one of the nation's basic industries, trucking.

Williams said yesterday that he hopes the talks with Trucking Management Inc., the bargaining arm for unionized trucking firms, will yield a new, 39-month agreement before the current three-year contract expires March 31. Neither he nor TMI officials would speak about specific wage proposals. But both sides publicly have called for wage moderation to help the trucking industry overcome serious financial difficulties caused by rising prices and trucking deregulation.

Unionized trucking firms complain that deregulation has made them vulnerable to nonunion carriers that generally operate with lower costs. Industry officials claim, and Teamsters leaders agree, that deregulation has helped kill many union firms, with a resultant loss of about 120,000 Teamster jobs since 1980.

TMI, anxious for financial relief, asked the union Aug. 27 to open negotiations several months earlier than scheduled. The union agreed Sept. 14, largely because "we have to do something to help the industry," Williams said then.

However, dissident rank-and-file Teamsters represented by the Teamsters for a Democratic Union vowed yesterday to oppose any move to reduce or eliminate cost-of-living agreements or to modify work rules in a way that could jeopardize job security. Rank-and-file distemper largely was responsible for the cancellation earlier this year of about 30 local contracts containing wage "rollbacks."

The union won a $1.50-an-hour wage increase in 1979 after a 10-day nationwide strike. The current average hourly wage for a Teamster trucker or warehouse worker is $12.96, excluding benefits.