"Initially, the beginning of June seemed to be a more realistic target, but [...] now it looks like we're going to start in May," he told a news conference.
More regular and more frequent vaccine deliveries have allowed the government to revise its vaccination strategy, according to Dulkys.
The Health Ministry plans to unveil its updated mass vaccination plan on Thursday.
Some municipalities have already started administering shots to people aged over 55 years, and Vilnius has begun giving the jab to those aged 44 and over.
Lithuania currently has over 211,000 unused vaccine doses, but some of these will be needed to administer second shots to people who have already received the first jab, according to Dulkys.
The country has received a total of 1,250,555 vaccines so far. All of them have been delivered to vaccination centers across the country and 1,039,032 have been administered, based on the latest official statistics.