He is expected to pledge closer ties between the US and Israel if elected.
The first leg of Mr Romney's trip, in London, was marred by controversy when he questioned whether the city was ready to host the Olympic Games.
After talking of "disconcerting" signs in London's preparations, Mr Romney backtracked and predicted a "very successful" Olympics.
A meeting with Palestinian Prime Minister Salam Fayyad is also scheduled, though not with Palestinian President Mahmoud Abbas.
The BBC's North America editor Mark Mardell says Mr Romney is highly critical of the international talks taking place which might lead to Iran being allowed to enrich some uranium. Mr Mardell wants zero enrichment.
In his speech on foreign policy, Mr Romney will say he hopes the military option on Iran can be avoided but that it should not be taken off the table.
Mr Romney says this is the best chance of focusing the minds of Iranian leaders on finding a peaceful solution.
A source in Mr Romney's campaign said he also agreed with those who worried the Arab spring could turn into an "Islamist winter", our correspondent says.