"This remains an ongoing effort," she told reporters at the White House on Friday.
She said Putin had responded to her letter earlier this year and that they remained in touch.
"President Putin and I have had an open channel of communication about the welfare of these children," she said.
"For the past few months, both sides have participated in several back channel meetings and calls."
The first lady said her representative was working directly with Putin's team to secure the safe reunification of children with their families between Russia and Ukraine.
Eight children had been returned to their families within the last 24 hours, she said.
President Trump has expressed frustration in recent weeks for not ending the war in Ukraine.
Ukrainian President Volodymyr Zelenskiy said on Friday that Russia deliberately waited for bad weather before staging a vast attack on Ukraine's energy system, adding the conditions reduced the efficiency of air defences by between 20 per cent and 30 per cent.
"The main assault was in four regions," Zelenskiy told reporters in Kyiv.
"I believe that the weather conditions affected our capability to repel by something like 20-30 per cent."
Russian drones and missiles struck Ukrainian energy facilities overnight, plunging parts of Kyiv into darkness, cutting power and water to homes and halting a metro link across the Dnipro river.
Ukraine's energy ministry said 380,000 customers were still disconnected on Friday afternoon.
"The blow is strong but it is definitely not fatal," he said about the strikes.
Zelenskiy said there were 203 energy facilities in the country which needed air defences to protect them from Russia.
He said Russian forces had attempted a new assault near the town of Dobropillia in eastern Donetsk region, where Ukrainian forces have reported successes in recent weeks, but had been repelled.
"The Russians tried to stage some offensive actions," he said.
"They wanted to unblock their troops but they suffered losses and retreated."
Zelenskiy also said Ukraine was waiting for clarification of the status of 10 air defence systems promised by the US.
He said he hoped the "coalition of the willing," a group of countries pledged to strengthen support for Ukraine, would hold a new meeting this month.
