Speaking to journalists as she travelled to Jordan, which she is visiting before travelling to Saudi Arabia, Mrs May said humanitarian aid was one of the issues she would be discussing on her trip.
"We are concerned about the humanitarian situation - that's why the UK last year was the fourth largest donor to the Yemen in terms of humanitarian aid - £103m. We will be continuing with that," she told the BBC.
"And yes, we will be raising the humanitarian issue. We believe it is important that we recognise the threat that there is in terms of people's lives. We will be supporting that through the aid and support that we give."
Mrs May said she would also be raising human rights issues with her Saudi hosts, adding that "if we have the relationship we are able to do that".
"So rather than just standing on the sidelines and sniping, it's important to engage, to talk to people, to talk about our interests and to raise, yes, difficult issues when we feel it's necessary to do so."
She also defended the drive to strike new trade links, saying the UK had "long-term and historic relationships" with Saudi Arabia and Jordan.
The countries, she said, were "important for us in terms of security, they are importance for us in terms of defence and yes, in terms of trade.
"But as I said when I came to the Gulf at the end of last year, Gulf security is our security and Gulf prosperity is our prosperity."
The PM was asked by the BBC's deputy political editor John Pienaar what "the May doctrine of foreign policy" was.
She replied that it was "that everything we do is in our British national interest".
"It's in our British national interest to have good relations around the world so we can trade around the world - that brings jobs and prosperity to the UK," she said.
"It's also in our national interest to ensure we're working with others around the world to maintain our safety and security - and yes, it's in our national interests to ensure that the values that underpin us as Britons are values that we promote around the world - and that's what we're doing.
Analysis - John Pienaar, BBC deputy political editor
Theresa May's mission to cultivate the friends and trading partners that Britain will need after Brexit continues as the prime minister heads into Saudi Arabia, and inevitably another controversy about the depth of Britain's commitment to the cause of human rights.
It's a relationship that's proved awkward for successive British leaders over decades. But now the continuing famine in Yemen, and civilian casualties from the Saudi-led - and UK-backed - blockade and attacks on rebel forces there have only raised the pitch of the controversy.
The prime minister's approach to relations with states like Saudi Arabia is seen by colleagues as hard-headed - critics say cold. In government - and among some who oppose the government on this - it's acknowledged that if Britain withdrew from lucrative arms deals, there's no shortage of competitors willing to oblige.
Shared intelligence in the fight against terrorism is said to have been valuable. And the PM's been keen to emphasise the British aid effort in Yemen. Yet some MPs - on the Conservative side too - dislike the sight of Britain supporting a blockade in Yemen, and seeking to relieve the suffering it causes at the same moment. Others simply argue that Britain is selling its principles for profit.
Asked about women's rights in Saudi Arabia, where - among other restrictions - women are not allowed to drive, Mrs May pointed to the changes promised as part of its Vision 2030 programme, adding: "I hope also that people see me as a woman leader will see what women can achieve and how women can be in significant positions."
Vision 2030's goals included increasing women's participation in the workforce from 22% to 30%.
She added: "I've talked to the Saudis on a number of occasions and raised issues of this sort. We have already seen some changes.
"One of the meetings I'm going to be having when I'm in Saudi will be with a female minister. I'll be meeting with her and talking to her about the role that she plays. And generally we do encourage people to look at women's role in society."
Mr Corbyn called for the immediate suspension of UK arms exports to Saudi Arabia.
He criticised the "dictatorial Saudi monarchy's shocking human rights record" and said the PM should focus on human rights and international law at the centre of her talks.
"The Saudi-led coalition bombing in Yemen, backed by the British government, has left thousands dead, 21 million people in need of humanitarian assistance and three million refugees uprooted from their homes," he said.
"Yemen urgently needs a ceasefire, a political settlement, and food aid, not more bombing.
"British-made weapons are being used in a war which has caused a humanitarian catastrophe."
As part of her visit, Mrs May is also setting out details of how a £1bn package to support victims of the fighting in Syria will be spent.
Downing Street said £840m announced last year and an extra £160m of new money would provide support for refugees and countries hosting them, including Jordan.
The investment will ensure refugees do not "feel forced to make the perilous and potentially life-threatening journey to Europe", Number 10 said.
It includes investment in education, skills and jobs.
Mrs May also announced that the UK will send military trainers to Jordan to help the country's air force in the fight against so-called Islamic State.