Ashton is on a visit to the rebel-held eastern town of Benghazi where she is due to open a EU mission office in a city hotel later on Sunday.
Speaking after a meeting with Mustafa Abdul Jalil, the head of the rebel National Transitional Council, NTC, she said the EU would support the rebels for as long as the country wanted them to be there.
“The people of Libya have spoken about the future they want,” she said. "I am here on behalf of all the 27 countries of the European Union to offer support to that future.”
The European Parliament has long argued for recognising the NTC, which so far has been recognised only by France, Italy, Qatar and Gambia.
Just hours ahead of Ashton's visit, Nato-led warplanes struck the Tripoli port and Kadhafi's immense compound of Bab al-Aziziya near the capital. There were two raids on the port and Bab Al-Aziziya which has already been targeted several times.
Meanwhile, US President Barack Obama sent a letter to Congress on Friday asking for political support of US action in the Nato assault, as he hit a technical 60-day deadline to get official congressional approval for use of his war powers.
Also, African Union leaders will gather for an extraordinary summit in Addis Ababa, Ethiopia, on Wednesday and hursday to discuss the Libyan conflict, the organisation announced.
Last month, the pan-African body proposed a truce but it was rejected by rebels, who insisted on Kadhafi's departure.