"Hezbollah is a member of the Lebanese society and it is represented in the Lebanese parliament and it will bear responsibilities," he said before leaving for Egypt at the end of a two-day visit to Lebanon.
Hajj Hassan told the AFP news agency that the meeting "means more EU overture towards Hezbollah, and one at a higher level."
"This also means better communication for the European Union with the region and its parties," he said, adding that the meeting will "move the EU towards more realism."
Hajj Hassan said he briefed Solana on what he called Israel's daily military flights over Lebanon in breach of UN resolutions, and the alleged Israeli spy networks in Lebanon.
Lebanese authorities have arrested about 100 people suspected of spying for or collaborating with Israel in the weeks leading up to the elections.
The lawmaker also told Solana that the sensitive issue of whether to disarm Hezbollah was being dealt with in broad political discussions led by President Michel Suleiman.
Hajj Hassan is among 11 Hezbollah candidates elected to the 128-seat parliament.
Solana said Lebanon's rival political leaders "realise the responsibility they face" and that he expected them to find a way "to push the country forward and form a cabinet" soon.
The March 14 pro-Western coalition that defeated the March 8 Hezbollah-led bloc in the June 7 general election could form a national unity government that includes Hezbollah..
Political groups in Lebanon have yet to agree on a defence strategy that could possibly include the integration of Hezbollah's arsenal of rockets into the Lebanese armed forces.