"We invited either their leadership or the foreign ministers to come and talk about these specific issues," Pranckietis told BNS by phone from Israel, referring to the idea of opening a Palestinian representation.
Lithuania would like the Baltic representation to be based in Vilnius, the speaker said.
"They (Palestinians) are sticking to this idea. They are discussing it and they said publicly that they'd like us, Lithuania, to contribute to their recognition," Pranckietis said, commenting on his conversation with Palestinian President Mahmoud Abbas.
"We said we were keeping to a two-state solution approach and, anyway, we couldn't ignore the EU's common position," he said.
The speaker said no thorny issues, such as the recognition of Jerusalem as the Jewish state's capital, had been brought up at his meetings with Israel's leaders.
"No sensitive issues were touched upon on their side. The atmosphere was very friendly," he said.
Pranckietis called for closer ties between Lithuania and Israel on security issues. He said his proposal that the Lithuanian parliament's Committee on National Security and Defense liaise with the respective committee of the Israeli parliament had been met with interest.
The speaker of the Seimas also said he had proposed that Israel discuss such issues as cyber-attacks or unconventional warfare with the Baltic and Nordic countries within the NB8 format.
As part of his trip to Israel, Pranckietis met with Yuli-Yoel Edelstein, the speaker of the Knesset, members of the Israeli parliament's friendship group and local Lithuanians.
He is also scheduled to visit the Yad Vashem museum and meet with organizations of Jewish immigrants from Lithuania in Israel.
Pranckietis is being accompanied on his trip by Vytautas Bakas, chairman of the Seimas Committee on National Security and Defense, Juozas Bernatonis, chairman of the parliament's Committee on Foreign Affairs, and MP Emanuelis Zingeris.
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