Ligi, a former Finance Minister and Defense Minister, took over from Marina Kaljurand in September after she decided on an ultimately doomed attempt to become Estonian president.
Ligi and Rinkevics expressed their like-mindedness on all topics, with Rinkevics saying "Our position is practically identical", particularly on the necessity of maintaining European Union sanctions against Russia unless there is "substantial progress" in implementing the Minsk agreements.
"What we have seen recently are not positive signals," Rinkevics said.
ForMins of Latvia & Estonia expressed strong support 4 full implementation of Minsk agreements during their joint press conference in Riga pic.twitter.com/N0omUYRfCG— Latvian MFA (@Latvian_MFA) October 5, 2016
Ligi said he hoped rather than expected the newly-elected Russian Duma would move forward with a formal border ratification treaty with Estonia so that his country could carry on strengthening infrastructure along its eastern border.
"We are waiting for the Russian Duma to do its homework," Ligi said, and alluded to the notorious kidnap of Estonian intelligence agent Eston Kohver from a borer area.
"They of course have their reasons on whether they adopt the law or not," Ligi said.