According to the Lietuvos Žinios daily, 12 protesters gathered outside the embassy and presented the embassy's employees with a letter to Lithuania's President Dalia Grybauskaitė.
Lithuania's Ambassador to Finland Arūnas Jievaltas told BNS he could not comment on the protest action.
"I cannot tell you anything, I attended a presidential inauguration yesterday. I only heard from my colleagues about somebody standing at the embassy's windows," the diplomat said.
Protest organizers said in their communiqué that the gathering was aimed at drawing the attention of the Lithuanian public and state institutions to the fate of six former foster children of the Gatayev couple who are currently in Vilnius.
"Gatajevs demand unlimited telephone communication with their foster children, have asked for opportunities for all members of the Gatayev family to meet the children. They also called for an opportunity for the children to learn the Chechen and Russian languages, culture of their home country and profess their religion," reads the statement.
The story of the Chechen couple, often called the Grozny angels, drew massive public attention following the 2009 rulings by Lithuanian courts.
In early 2009, a court in Kaunas found the couple guilty of violent treatment of their foster children, murder threats and overstepping their rights. They were each sentenced to 10 months in prison.
In September 2009, Another Kaunas court extended the sentence to 18 months. The Gatayevs disappeared after the verdict. The authorities announced their search and started extradition procedures. The spouses were detained in Finland in early January last year.
Human rights defenders said there were possible violations in the case - media quoted cases of interference by the State Security Department and possible involvement of Russia's special services.