On Sunday, Montenegrins voted for independence from the state union with Serbia.
"The purpose of the talks should be to maintain and further bilateral relations as well as relations in the region," Lajcak said during his talks with Montenegro's President Filip Vujanovic on Monday.
The local media quoted Lajcak as saying that the pre-referendum campaign in Montenegro was in accordance with high democratic standards.
"The referendum day was in accordance with those standards as well, which confirms Montenegro's maturity," the EU diplomat said.
Lajcak also held talks with Montenegrin Parliament Speaker Ranko Krivokapic and the leaders of the pro-union bloc who still refuse to concede defeat until the announcement of final results.
The head of the pro-independence bloc, Montenegrin Prime Minister Milo Djukanovic, said that the international verification of official preliminary results would start in the course of the day.
He said that it was very important for Podgorica to see that neighbouring countries did not view Montenegro as a factor of destabilisation.
In the coming period the country's priority will be to resume negotiations with the European Union so that Podgorica and Brussels could sign a Stabilisation and Association Agreement by the end of this year, Djukanovic said.
Montenegro will pursue its policy of good neighbourly relations with countries surrounding it in order to help strengthen cooperation and stability in the region, he added.