The U.S. Treasury said that Lew warned Russian Finance Minister Anton Siluanov that the United States is prepared to impose "additional significant sanctions" if Russia escalates the Ukraine situation. Treasury said in a statement that Lew described Russia's annexation of Crimea as "illegal and illegitimate."
Lew's discussions with Siluanov came in advance of meetings Thursday of finance officials from the Group of Seven major industrial countries and the Group of 20 nations, which includes the G-7 countries and emerging economies such as China, Brazil and India.
Russia is a member of the G-20 but not the G-7. The G-7 nations are the United States, Japan, Germany, Britain, France, Canada and Italy.
Last month, President Barack Obama met with other G-7 leaders and the group confirmed that it was indefinitely suspending co-operation with Russia, which for more than a decade had joined with the G-7 countries to form the Group of Eight nations. That larger group was to hold a summit later this year in Sochi, Russia. But the G-7 nations have said they will boycott that meeting.
It was unclear how much support the United States would receive from other countries to strengthen the sanctions imposed on Russia.
After the G-7 talks, the group issued a joint statement that confirmed that the situation in Ukraine had been discussed, including the country's financing needs, but the statement did not indicate that the group had endorsed tougher sanctions.
French Finance Minister Michel Sapin told reporters before the discussions that France preferred to focus on the economic support being provided to Ukraine. That effort is being led by the International Monetary Fund, which says it will provide up to $18 billion in loan guarantees to Kyiv to help the country get its economy moving again.
"The question is not to talk about sanctions. The question is to get started ... as quickly as possible" working to get the IMF's support program implemented.
The U.S. delegation to the G-7 and G-20 talks was led by Lew and Federal Reserve Chair Janet Yellen.
A G-20 dinner Thursday night included a tribute to former Canadian Finance Minister Jim Flaherty, who died earlier in the day. Flaherty, who took the Cabinet position in 2006, was the longest-serving G-7 finance minister before he announced three weeks ago that he was stepping down. A friend said he had died of a massive heart attack.
Australian Treasury Minister Joe Hockey, the current chair of the G-20, told the group, "Canada is poorer for his passing and we are all poorer."
In the G-7 statement, the group praised Flaherty as "a greatly valued and forthright colleague and friend."
Lew cited Flaherty for his skill in helping Canada navigate the 2008 global financial crisis.
The G-20 talks were scheduled to wrap up Friday with news conferences from many of the participating nations. Then on Saturday, the policy-setting councils of the 188-nation IMF and its sister lending organization, the World Bank, were to hold their spring meetings.
On Thursday, IMF Managing Director Christine Lagarde said the global economy was finally turning the corner after a deep recession but the recovery remains too weak.
Speaking at a news conference, Lagarde called on governments to aggressively pursue programs to spur economic growth to help the millions of people who remain unemployed.
"Bold actions are need to generate stronger growth," Lagarde told reporters.
The discussions on how to boost growth and fight poverty were likely to be overshadowed at the meetings by the rising tensions over Russia's actions in Ukraine.
The United States and European nations have imposed various economic sanctions on Russia including travel bans and asset freezes in response to Russia's annexation of Crimea, with the possibility of tougher sanctions on the table.
To provide support for Ukraine's cash-strapped government, the IMF is working up a loan package to provide between $14 billion to $18 billion in assistance.
However, Russian President Vladimir Putin has threatened to demand advance payment from Ukraine for natural gas that Russia supplies to the country.
Asked Thursday about the IMF support, Lagarde said the IMF hoped to have the program for Ukraine approved by its 24-member board by the end of this month or early May.
Foreign ministers from the 28-nation European Union are scheduled to meet in Brussels on Monday and the issue of expanding the sanctions will be discussed. However, some countries have already expressed opposition to such a move.
World Bank President Jim Young Kim told reporters at a separate news conference that the sanctions that have already been imposed were having a dampening effect on Russia's economy and if the crisis worsens, he said Russia could be pushed into a recession.
Kim said that the World Bank was preparing its own support package for Ukraine amounting to around $3.5 billion.
Associated Press writer Harry Dunphy contributed to this report.