She said the government was working closely with the US Congress to get the necessary legislation passed.
Mrs Clinton was speaking ahead of the Asia-Pacific Economic Co-operation (Apec) summit in Vladivostok.
Russian President Vladimir Putin has urged a fight against protectionism to turn the global economy around.
And Chinese President Hu Jintao promised his country would try to help the world’s economy by increasing the demand in China for imported goods.
‘Bridges not walls’
Although Russia is now a member of the World Trade Organisation, there is still a piece of legislation that prevents US companies trading normally with Russia – the 1974 Jackson-Vanik amendment which, although suspended, remains in place.
Introduced in 1974 to put economic pressure on the Soviet Union, so as to encourage the communist leadership to allow Jewish people to emigrate, it somehow remains on the American statute book.
Since Russia’s citizens are now free to leave any time, and as the country has just joined the World Trade Organisation, it seems to many in Moscow to be perverse that the Jackson-Vanik amendment remains.
But some US congressmen do not want to repeal Jackson-Vanik without introducing a new piece of legislation to keep up the pressure on Russia to improve human rights.
Many of them favour the Magnitsky Act, named after a young Russian lawyer who died in prison in suspicious circumstances. The Magnitsky Act would create a list of Russian officials who are banned from the United States on human rights grounds.
President Obama’s administration – which has been trying to improve relations with Russia – is against the Magnitsky Act.
She added: “To make sure our companies get to compete here in Russia, we are working closely with the United States Congress to terminate the application to Jackson-Vanik to Russia and grant Russia permanent normalised trade relations.
“We hope that the Congress will act on this important piece of legislation this month.”
However there are concerns in the US Congress about Moscow’s support for Iran and Syria, as well as its broader human rights record, so the timing of a vote on the issue remains unclear.
Mr Putin, who is hosting the summit, expressed concern about the world economy, and particularly Europe’s debt crisis.
“The priority goal is to fight protectionism in all its forms. It is important to build bridges not walls,” he said.
President Hu said: “The world economy today is recovering slowly, and there are still some destabilising factors and uncertainties.
“The underlying impact of the international financial crisis is far from over.
“We will work to maintain the balance between keeping steady and robust growth, adjusting the economic structure and managing inflation expectations. We will boost domestic demand and maintain steady and robust growth as well as basic price stability.”
Meanwhile, Australian Prime Minister Julia Gillard has left the talks early to return home after her father died.