May has come under harsh criticism over her Saudi visit, facing calls at home to raise rights issues with local leaders.
The visit also comes less than a week after Britain officially started a two-year countdown for quitting the European Union.
May has said that economic issues were a priority on her trip, but maintains she will not shy away from addressing "hard issues" on foreign visits.
The British premier on Tuesday met Crown Prince Mohammed bin Nayef, the country's interior minister and first in line to the throne, and discussed "joint cooperation in combating extremism and fighting terrorism", state news agency SPA said.
She is scheduled to meet King Salman on Wednesday.
May began her three-day Middle East tour on Monday in Amman, where she touted cooperation in the fight against the Islamic State jihadist group.
Jordan and Britain are part of the US-led coalition that has been carrying out air strikes and supporting local forces against IS in Syria and Iraq since mid-2014.
May has said she would be looking to use the "immense potential for Saudi investment to provide a boost to the British economy" during her trip to the region.
Britain is looking to strike new trade deals as it prepares to leave the EU, with a major focus on longtime partners such as the energy-rich Gulf states.
Qatar, a longtime investor in Britain, announced plans last month to invest £5 billion ($6.23 billion/5.8 billion euros) within five years.
Saudi Arabia is Britain's largest trading partner in the Middle East, with exports of more than £6.5 billion in British goods and services to the country in 2015.
Riyadh is also looking at boosting its foreign investments as part of a long-term plan known as "Vision 2030", which aims to diversify the economy and reduce dependence on oil revenues.
- Call to halt arms sales -
Signup to our newsletter and follow us on Facebook and Twitter!
May came under fire ahead of the visit, with opposition Labour Party leader Jeremy Corbyn demanding she raise concerns about "the dictatorial Saudi monarchy's shocking human rights record".
He called on Britain to halt arms sales to Riyadh immediately and to push for a ceasefire in Yemen, where Saudi Arabia has for two years led a Gulf military campaign against Iran-backed Huthi rebels.
More than 7,700 civilians have been killed and a further 42,500 wounded since the start of the campaign, according to the United Nations. Seven million Yemenis face starvation.
Rights groups including Amnesty International and Human Rights Watch have called for an end to arms sales from Britain and the United States to Saudi Arabia over the coalition's actions in the Arabian Peninsula state.
Saudi Arabia has bought more than $5 billion (4.7 billion euros) worth of arms from the US and Britain, according to the Stockholm International Peace Research Institute think tank.
- 'Woman's role in society' -
May, who eschewed the local custom of women wearing headscarves in public upon arriving in Riyadh, has also faced questions around her stance on women's rights in ultra-conservative Saudi Arabia -- the only country where women are not allowed to drive.
She has said she hopes to be an example of the role women could play in any society.
"I hope that people see me as a woman leader, will see what women can achieve and how women can be in significant positions," May told the BBC ahead of her trip.
May on Tuesday met Sarah al-Suhaimi, head of the Saudi stock exchange Tadawul. Suhaimi, also CEO of NCB Capital, is the first women to head a Saudi investment bank.
On Wednesday, May is slated to meet Princess Reema bint Bandar, head of the women's section at the General Authority for Sports.
Saudi Arabia recently announced it planned to increase women's participation in the workforce from 22 to 28 percent by 2020.
Local media outlets have also reported that the kingdom will open women-only gyms.