She said that both Arabs and Israelis were "members of the same camp", facing threats from groups such as Hezbollah and Hamas.
She also said she hoped "other Arab states will follow the example of Qatar" in maintaining ties with Israel.
Qatar has low-level trade relations with Israel, but no formal diplomatic ties.
High-level meeting
Livni arrived in Doha on Sunday, where she was due to meet Sheikh Hamad bin Khalifa Al Thani, Qatar's emir, and Sheikh Hamad bin Jassem bin Jabr Al Thani, who is both the country's prime minister and foreign minister.
Sheikh Hamad bin Jassem said talks with Livni would focus on ways of calming the situation in the Gaza Strip.
"This, of course, will be our main preoccupation and the main issue we will discuss with Livni," he said.
"But I don't want to put this in the context of a mediation," he said, when asked if Livni's presence meant that Qatar was trying to mediate between Israel and Hamas.
While in Doha, Livni also held a meeting with Yusef bin Alawi bin Abdullah, her Omani counterpart, to give him "an update on the negotiations with the Palestinians", according to an aide.
The Israeli foreign ministry said that Livni's meeting with Oman's top diplomat was their first public encounter.
Contacts between the Gulf and Israel do happen, but are uncommon at such a high level and in such a public forum. On the other hand, Doha has good diplomatic relations with Tehran.