"I'll definitely initiate discussions. I've already said that we have to initiate discussions on these and similar issues and if one part of our society wants to talk about it, then I, as the minister, must initiate discussions," Jankevičius told BNS on Thursday.
"Following these discussion, (...) the government will discuss all 'for' "and 'against' and we'll then make a decision," he added.
Liberal politicians in Lithuania have repeatedly tabled proposals to legalize civil partnership of same-sex couples, but these initiatives never reached the adoption stage at the parliament.
Those in favor of regulating by law same-sex relationship say that homosexual couples in Lithuania are now discriminated against, because such people have no right to inheritance or automatic access to information about their partner's health in an emergency, and they cannot represent each other in court proceedings.
Opponents say that if partnership is legally recognized, this will undermine marriage as an institution and may be the first step toward allowing homosexuals to adopt children.
Human rights experts also criticize Lithuanian politicians for failing to ensure better access for transgender people to medical services.
Jankevičius would not say what his position on these issues is.
"Since my words are treated as those by the minister, I'll make my position known after discussions," he said.
Lithuania this year scores better in a survey on LGBT rights, but still lags behind many EU member countries.
ILGA-Europe this year ranked Lithuania 37th out of 49 countries in its annual report, up from 39th place last year.
Latest opinion polls show that 11 percent of Lithuanians support same-sex partnership and 7 percent approve of legalizing homosexual marriage.