Lew said in a San Francisco speech just after a trip to Beijing that the United States would embrace any new international development bank providing it "complements" existing institutions like the World Bank and International Monetary Fund.
He also stressed that new institutions needed to "share the international community's strong commitment to genuine multilateral governance and decision making, and ever-improving lending standards and safeguards," according to his prepared speech.
Washington, worried about a China-dominated AIIB cutting into the work of the World Bank and Asian Development Bank -- where the US is the leading voice -- at first sought to persuade its allies to hold off from joining the banks.
But in recent weeks most European powers and other leading economies have signed on to the new institution, guaranteeing it a strong capital base and isolating the US position.
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That has left washington appearing isolated in not wholeheartedly welcoming Beijing's creation.
Speaking at the northern California chapter of the Asia Society, Lew said he was encouraged that Chinese leaders "made clear that they aspire to meet high standards and welcome partnership."
If the AIIB works with existing institutions to finance infrastructure projects around Asia, Lew said, it "will help demonstrate a commitment to the highest standards of governance, environmental and social safeguards, and debt-sustainability."
Lew still did not let on if the United States would join the AIIB.
He made clear Washington still supports the mission of the World Bank, the International Monetary Fund and other older regional development banks, and is concerned about how Beijing will proceed with a new institution poised somewhat as a rival to those.