Key parts of the UK's immigration policy - including on foreign students and doctors coming to the UK - will be reviewed, the home secretary has said.
Sajid Javid told the BBC there was a "perception problem" over the decision to include students in net migration figures.
And he said he would "think more carefully" about the cap on the number of skilled workers given visas.
Mr Javid became home secretary in April after Amber Rudd quit.
Speaking to the Andrew Marr Show, he also said he would be lobbying Chancellor Philip Hammond for more cash for policing, and confirmed an increase in security officers to boost counter-terrorism efforts.
However, Mr Javid said that addressing the issue of the Windrush scandal, which led to Ms Rudd's resignation, would be his top priority.
He told the Marr show that changes had already been made to the "hostile environment" approach to illegal immigration, which critics say was responsible for the problems.
These changes included rethinking restrictions on illegal migrants' rights to open bank accounts, he said.
Mr Javid also said seven members of the Windrush generation who were wrongly deported had been contacted so far, with efforts under way to reach a further 24.
On the wider approach to immigration, Prime Minister Theresa May has faced repeated calls to exclude foreign students from the government's drive to reduce net migration into the UK, including from Scottish Conservatives leader Ruth Davidson.
Mr Javid said he understood criticism of the policy, and that he did "empathise" with the view that it did not sound very welcoming.
He said that although if students eventually left the country it should have no long-term impact, "there is a perception problem around this," adding: "It's something I've long considered."
It is "something I would like to look at again", he said.
'I see the problem'
The home secretary was also asked about the cap on so-called Tier 2 visas, introduced by Mrs May when she was home secretary as a means of limiting the number of skilled workers from outside the European Union who had a job offer.
The annual 20,700 cap has led to thousands of IT specialists and engineers as well as NHS staff being denied visas.
"I see the problem with that," Mr Javid said.
"It is something that I'm taking a fresh look at. I know a number of my colleagues certainly want me to take a look at this, and that's exactly what I'm doing.
"And I hope to think about this more carefully and see what can be done."
Lib Dem home affairs spokesman Sir Ed Davey said: "The home secretary will have the support of almost everyone in Parliament to exclude students and medical staff from the immigration cap, but it's far from clear that the prime minister is willing to admit her long-cherished policy is wrong."
Mr Javid also refused to explicitly endorse another immigration policy, the promise to reduce net migration below 100,000, saying he was committed to the Conservative manifesto which contained the pledge.
And he reiterated calls for more funding for frontline police officers.
The government had not yet started its spending review for the police, he said, adding: "But when we do, I'm sure the chancellor will learn of my views."
Labour responded by saying Mr Javid had "let slip that there is still no new money for our over-stretched police forces".