U.S. Secretary of State Rex Tillerson and Russian Foreign Minister Sergei Lavrov discussed rising violence in eastern Ukraine, with Tillerson asking Russia to "lower the level of violence," a U.S. State Department spokeswoman said Wednesday.

The two men, who spoke by telephone on Tuesday, also agreed to continue diplomatic efforts to address North Korea's nuclear program, emphasizing that neither Washington nor Moscow accepted Pyongyang as a nuclear power, spokeswoman Heather Nauert said in a statement.

They also addressed the crisis in Syria, she added.

The Russian foreign ministry on Tuesday said Lavrov told Tillerson that "Washington's aggressive rhetoric" had heightened tension on the Korean peninsula and was unacceptable.

Lavrov on Monday called on the U.S. and North Korea to start negotiations, adding that Russia was ready to facilitate such negotiations.

Russia and China have the relatively closest diplomatic relations with insular North Korea, which poses a nuclear threat to its neighbor South Korea and that country's allies Japan and the U.S.

Last week Russia and China voted in favor of a U.S.-proposed measure in the U.N. Security Council to impose additional economic sanctions on North Korea as part of an escalating effort to clamp down on that country's nuclear program.