Speaking in the House of Commons, James Brokenshire said giving a guarantee that EU citizens living in Britain can stay would "pre-empt" discussions about the status of UK citizens living in European Union (EU) countries.
"It has been suggested the government could now fully guarantee EU nationals living in the UK the right to stay," he said.
"This would be unwise without a parallel assurance from European governments regarding British nationals living in their countries.
"Such a step might also have the unintended consequence of prompting EU immigration to the UK. It is in the best interests of all that the government conducts detailed work on this issue and that the new prime minister decides the best way forward as quickly as possible."
Despite not offering a guarantee, Mr Brokenshire said EU nationals continue to be welcome in Britain and "their right to enter, work, study and live in the UK remains unchanged" since the country voted to leave the EU on June 23.
As the final split from the EU may be a process that takes several years, Opposition politicians want the government to make a formal announcement to ease the uncertainty faced by some three million EU citizens living in Britain.
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Labour legislator Gisela Stuart said Monday that it was wrong to make Eu citizens a "bargaining chips" in negotiations.
She said it was “deeply, deeply offensive” to not give clarity to millions of people who may be planning for the next couple of years.
Andrea Leadsom, a junior minister, offered reassurance to EU nationals currently living in Britain: "I commit today to guaranteeing the rights of our EU friends who've already come here to live and work. We must give them certainty."
Shadow home secretary Andy Burnham said the EU nationals living in Britain, who arrived with the expectation they could remain in the country, were having the “rug pulled from under them”
“The three million or so EU nationals living here are the fathers and mothers, aunties and uncles, grandmas and grandads of millions of British children,” Mr Burnham said.
“Any uncertainty hanging over their right to be here is tantamount to undermining family life in our country.”
Divorce process
Despite the 52 per cent referendum vote, Britain has not yet invoked Article 50 of the EU's Lisbon Treaty to begin the formal process of breaking away. While all the candidates to succeed Cameron say there is no going back, some anti-Brexit politicians say it is still not a foregone conclusion.
Law firm Mishcon de Reya said on Monday it had started legal action to demand the government win approval from parliament before triggering the divorce process.
Most of the 650 members of the House of Commons opposed Brexit before the vote.
"The outcome of the Referendum itself is not legally binding and for the current or future Prime Minister to invoke Article 50 without the approval of Parliament is unlawful," Kasra Nouroozi, a partner at Mishcon de Reya, said in a statement.
Former defence minister Liam Fox, a pro-Brexit figure and an outsider in the leadership contest, said Britain should activate article 50 before the end of the year, and he did not believe any parliament vote was needed.
He said the free movement of people across Europe - a core principle of the EU but a major concern for many Britons - should not be on the table in negotiations about a trade deal with the EU after Brexit.
"It is quite clear that the public rejected the concept of free movement, and that the price of including such free movement as part of a trade deal would be regarded as a betrayal by the British people," Fox said.
The other leadership contenders are work and pensions minister Stephen Crabb and justice minister Michael Gove, a Leave campaigner who caused high political drama last week by turning against his ally, former London mayor Boris Johnson, and driving him from the race.
