Most U.S. business groups have not weighed in on Thursday's historic vote by the U.K. to leave the European Union, but a few have issued statements in an attempt to calm public fears as the stock market takes a beating with the news.

In a statement, the International Swaps and Derivatives Association acknowledged the vote was "a momentous decision and will have significant implications for financial markets." However, it also sought to reassure the public that it would work with members to keep the derivatives market functioning safely and efficiently.

"It is important to stress, however, that the U.K. vote to leave the EU will not have an immediate impact on the legal certainty of existing derivatives contracts, nor will it require any immediate contractual change or action from counterparties," ISDA said.

"Once the U.K. government serves formal notice of its intention to withdraw, the U.K. will continue to remain a member of the EU for at least two years," the association added. "During that time, existing European treaties, directives and regulations will remain in force."

ISDA is planning on holding a webinar Wednesday for members on what to expect now the vote has taken place. The group will also hold a media briefing that same day.

U.S. Chamber of Commerce CEO Thomas Donohue said in a statement the British people have opted for change, but whether the vote will ultimately be beneficial to the U.K. will depend on what choices policymakers make in coming months.

"While some uncertainty is unavoidable in the near term, the first order of business will be to reassure investors about those choices and avoid precipitous action in the coming negotiations with the EU," he said.

Financial Services Roundtable CEO Tim Pawlenty also acknowledged the vote took markets "into uncharted waters."

"Since markets don't like uncertainty, market volatility could prevail for a while but the U.S. financial system has taken major steps to prepare for and navigate through new challenges and it is well-positioned to continue to serve and help customers," Pawlenty said. "Individual investors should seek the advice of professional investment advisors as they contemplate the implications of these events."

National Association of Federal Credit Unions Chief Economist Curt Long said in a statement he also saw the likelihood of increased volatility in U.S. financial markets, but noted that Federal Reserve action is likely on hold until at least the fourth quarter of 2016.

"As for credit unions, they should prepare for the present interest rate environment to persist for some time as normalization is bound to proceed on an even more gradual path than the Fed has previously indicated," Long said. "Credit unions are also likely to see a repeat of the second half of last year when market volatility led to a surge in share growth."

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