Šimonytė promised to take "political leadership" on the citizenship retention issue after the referendum failed to receive enough "yes" votes on Sunday to pass.
The constitutional amendment would have allowed Lithuanian citizens by birth to keep their Lithuanian citizenship after acquiring the citizenship of another country.
"The problem is still there. We are still faced with the fact that many people are caught between a rock and a hard place. If elected, I'd rally support from political forces for the decision, which I believe should be adopted in the next referendum," she said.
The referendum on amending Article 12 of the Constitution, which would have expanded dual citizenship, had a turnout of 52.3 percent and is considered valid.
An overwhelming majority, 71.7 percent, of the votes were cast in support of allowing expatriate Lithuanians to keep their Lithuanian passports when they become citizens of another country. However, this did not cross the required threshold of 50-percent of the entire electorate for the motion to pass.