The Reagan administration yesterday warned its Ottawa summit partners that Europe's growing dependence on natural gas from Siberia could give the Soviet Union excessive influence over their economies.

In testimony before the congressional Joint Economic Committee, Undersecretary of State for Economic Affairs Myer Rashish said that, while the United States seeks "a prudent" level of economic relations with the Soviet Union and Eastern Europe, care must be taken to make sure that exports "do not contribute to the military potential of the recipient country."

Rashish said that the Soviets may be gaining "unhealthy influence" by creating a Western European dependency on supplies of natural gas. The potential disruption to Western Europe's economies, he said, was a danger comparable to "the more obvious example" of disruption of oil-supply lines from Middle East producers to Western consuming nations.

Rashish's statement was the most explicit statement thus far of the U.S. intent to raise delicate questions relating to East-West trade at the Ottawa summit.The United States is anxious for a new understanding on the sale of strategic materials and high-technology knowhow to the Soviets -- a policy that is expected to be further elaborated in a formal briefing today by Secretary of State Alexander Haig.

Europeans, notably West Germany, are anxious to expand their purchases of natural gas from Siberia, and worry that U.S. pressures to be circumspect may affect their overall commercial dealings with the Soviet Bloc. On Monday, European Communities Commission President Gaston Thorn observed on this issue that "the major problem is that what may be good for you may be a problem for us."

But Rashish said in his testimony that "the U.S. cannot have an effective policy on trade with these [Eastern] countries unless our policy is in harmony with that of our major trading partners. We need to achieve a common perception of the balance between security and commercial interests for the Western allies as a whole."

Rashish, who has been named President Reagan's personal representative for summit preparation, also said that while oil price rises have been a matter of economic concern and inflationary pressure, "it is the national security implications of the unhealthy dependence of the United States, and other major industrialized countries that are most disturbing to this administration."

In sharp contrast to the Carter administration's policy, the Reagan administration is stressing -- among other policy initiatives -- the importance of filling the Strategic Petroleum Reserve, Rashish said.

In response to a demand by Rep. Henry S. Reuss (D-Wis.) that Reagan accede to European pressure for lower American interest rates, Rashish intimitated that European countries are less disturbed by the American economic policy than is suggested in statements by their politicians.

As for the recent suggestion made by some European critics of American economic policy that the "mix" here should be changed by watering down the tax cut, thus reducing the burden on monetary policy, Rashish said he doubted that "the small marginal adjustments on taxes that are politically feasible can have any but marginal impact on interest rates."