During a visit to Israel, she has also extended an invitation to Prime Minister Binyamin Netanyahu to become the first Israeli prime minister to visit Australia.
Ms Bishop is on a visit to Israel and the Palestinian Territories.
She is also meeting Palestinian National Authority prime minister Rami Hamdallah and senior Palestinian security figures before travelling on to Europe.
Israeli prime minister Binyamin Netanayahu had warm words for Julie Bishop on her first full visit to Israel as foreign minister. "I just want to greet you and say that your friendship is terrific -- Australia's, the government's and yours personally. And we appreciate our friends."
Ms Bishop's response was equally warm: "Prime Minister, I am absolutely delighted to be here in Jerusalem. And I want to take this opportunity to reaffirm our absolute enduring commitment to the state of Israel and our friendship and invite you to come to Australia. And we're thinking there's a little window of opportunity early next year maybe? And the Australian public would warmly embrace you, welcome you, and we would look forward to the first visit of an Israeli prime minister ever to Australia."
It was an invitation Mr Netanyahu immediately accepted.
It is Julie Bishop's third visit to Israel.
She was previously there in 2008 as deputy leader of the opposition and again in 2014 for the funeral of Israeli prime minister Ariel Sharon.
Australia was one of the first countries to initiate full diplomatic ties with Israel after its establishment in 1948.
Ms Bishop says Australia will continue to stand by Israel in the international arena.
"We consider Israel a firm friend, as Israel may consider Australia a firm friend. We are one of a very small handful of countries that continues to take a stand in multilateral fora when there are obviously biased, discriminatory, unfair resolutions that are put forward. And we will continue to do that under our Government."
Israeli president Reuven Rivlin has acknowledged the support.
"And we consider the friendship between Australia and Israel as a friendship between great friends."
Bilateral cooperation, discussion of regional security and the Middle East peace process were also on the agenda.
Earlier, Ms Bishop paid her respects at the Yad Vashem Holocaust Museum in Jerusalem .
And in Tel Aviv, she visited Australia's so-called innovation "landing pad."
She says it is helping Australian entrepreneurs tap into Israel's well-developed science, research and innovation industry.
"Our relationship has the potential to enter into new fields of endeavour, particularly in innovation, where Israel is a world leader. "
During her meeting with Mr Netanyahu, Ms Bishop has also raised the case of World Vision Gaza director Mohammed El-Halabi.
Mr Halabi has gone on trial in a secret court, accused of diverting millions of dollars of donations from governments, including Australia, to the Palestinian organisation Hamas.
World Vision says it has found no evidence to back up the allegations.
Its Australia chief executive, Tim Costello, has told the ABC there is concern Mr Halabi will not get a fair trial.
"The charges allege that he diverted far more money than World Vision ever had in its program in Gaza, let alone money that he had access to, so we really are confused. So we need an open trial to actually understand what has gone on and see evidence."
However, Ms Bishop says closed proceedings are not unknown in legal systems around the world.
