Just weeks after becoming President Obama’s top outside adviser on reducing joblessness, General Electric chief executive Jeff Immelt faced two major public relations crises.

First, a nuclear plant in Japan using GE technology was at risk of melting down. Then, a news report raised questions about why GE paid no federal taxes last year.

With that as the background, Immelt made his first speech on Thursday as chairman of the President’s Council on Jobs and Competitiveness before the Economic Club of Washington.

He addressed the controversy over the company’s tax payments by saying that though “like any American we do like to keep our tax rate low,” GE follows all the rules. He repeated GE’s line that the company suffered huge losses during the financial crisis, accounting for minimal tax bill.

And he called for changes to the corporate tax system — an emerging item on Obama’s agenda — that would reduce tax rates, cut loopholes and ensure companies are only taxed on their U.S. operations.

“Business rarely speaks with one voice on anything, but we do on taxes,” he said.

In addressing concerns about Japan’s nuclear disaster, Immelt noted that GE technology had been installed in the Japanese nuclear reactors many decades ago, and he was not concerned that GE could be liable for damages.

For the most part, Immelt repeated refrains about what the country — and corporate America — needs to spur the economy and make sure U.S. companies rival those abroad: better education, especially in the sciences; investments in infrastructure; free-trade agreements; and immigration reform.

Immelt also gave a little new information on the operation of the council, a mix of executives, economists and labor leaders.

He said six working groups had been formed around themes: jobs, infrastructure, job creation through innovation, regulation, high-tech workforce and tax reform. And he said there would be a continuing focus on generating jobs by creating new businesses, particularly small businesses.

Immelt faced more heat on Thursday from liberal groups, who had released a statement of concerns the day before. Justin Ruben, executive director of MoveOn, said: “The fact that Immelt holds a high-profile administration position is shameful. Between dodging taxes, closing factories and cutting pay and benefits for workers while lavishing executives with huge pay raises, GE represents all that is wrong with corporate America and their influence in Washington.”

White House press secretary Jay Carney responded to Immelt’s critics on Wednesday. “I would say that membership on the Jobs Council, as the president made clear, is not decided by agreement on every issue,” Carney said.