Addressing a joint press conference, Plevneliev said that the two countries were cooperating very well within the European Union and NATO and shared many views.
Bulgaria and Croatia support the Euro-Atlantic integration of all countries in Southeast Europe and are ready to work together on long-term peace, stability and development in this part of Europe, he said.
Speaking of priorities in advancing cooperation, the Bulgarian president cited energy security and independence, saying that this required diversification of supply routes, a better connection between electricity and gas networks, and development of transport infrastructure.
Grabar-Kitarovic supported Bulgaria's initiative to establish an energy exchange for Southeast Europe.
She said that a summit would be held in Dubrovnik this August as part of her Adriatic-Baltic-Black Sea initiative at which regional energy cooperation would be one of the important topics. Before that, a Croatian representative would visit all the countries in the region to work out how EU funds could be secured for that purpose in the next EU multiannual framework. A regional programme for energy and transport infrastructure projects is also being considered.
An LNG terminal on the northern Croatian island of Krk and an Adriatic-Ionian gas pipeline will also play an important role, Grabar-Kitarovic said.
Plevneliev supported the Adriatic-Baltic-Black Sea initiative, which the Croatian president has been advocating as a new way of cooperation between Central European countries along the north-south axis.
Bulgaria plans to set up a gas hub at the Black Sea city of Varna that will also include an LNG terminal, and this project is being finalised in cooperation with the European Commission to ensure that it is in line with EU rules. Bulgaria has been advocating this project since late 2014 when Russia abandoned the South Stream gas pipeline project because of opposition from the the Commission.
The regional gas hub, called Balkan, will be fully owned by Bulgaria and is expected to be built with EU financial support. Gas would be supplied from Russia, Azerbaijan and Turkmenistan, as well as from Bulgarian and Romanian gas fields.
Croatia and Bulgaria are also cooperating in preparations for joining the Schengen zone. Grabar-Kitarovic said that on July 1 the Commission would start an evaluation that would last about a year, based on which it will be assessed whether Croatia meets the Schengen membership criteria.
Bulgaria has been very successful in using EU funds, with an absorption rate of 80 percent, and can help Croatia with its experience. Grabar-Kitarovic said she was not satisfied with Croatia's rate of absorption of EU funds, expressing hope that Croatia would soon be as successful as Bulgaria, which drew EUR 8.8 billion from EU funds from 2007 to 2013.
Speaking of bilateral economic relations, Grabar-Kitarovic said they were "rather modest" and needed improving. She noted that Bulgaria ranked 27th among Croatian foreign trade partners, with trade reaching a mere EUR 163 million in 2015.
Bulgarian investments in Croatia are almost non-existent, while last year Croatian investments in Bulgaria totalled EUR 14.5 million.
Bulgarian and Croatian enterprises are interested in stronger cooperation in energy, transport infrastructure, tourism, information and communication technologies, defence, the food industry, and agriculture.
The two presidents also discussed the migrant crisis and the fight against terrorism in light of last year's terrorist attacks in Paris and recent attacks in Brussels. They were agreed that a common European approach and solidarity were necessary, that there should be closer cooperation between national intelligence agencies, and that the root causes of the Middle East crisis needed to be addressed.
Grabar-Kitarovic stressed that migrants should not be equated with terrorists, calling for their integration and education as opposed to assimilation or isolation in ghettos and refugee camps.
The Croatian and Bulgarian presidents are scheduled to address a Bulgarian-Croatian economic forum on Thursday.
During her visit, Grabar-Kitarovic is due to deliver a lecture on European solidarity and meet with Croatian-language students. She is also scheduled to meet with Prime Minister Boyko Borisov, as well as with representatives of the Croatian community in Bulgaria.
Plevneliev visited Croatia in April 2015. He was the first head of state to meet Grabar-Kitarovic after she took office.