"The prime minister is fully committed to bringing overall numbers down," his spokesman said after official statistics showed net migration rose to an estimated record of 504,000 in the year to June.
"We're considering all options to make sure the immigration system is delivering."
"The United Kingdom has a long, proud tradition of providing a home for people fleeing persecution and oppression," junior British justice minister Mike Freer told the UN Geneva assembly earlier in November.
"However, our immigration and asylum systems and processes have been subject to significant strain over the last decade and continue to face enormous challenges," he said.
Interior Minister Suella Braverman last week caused fury by describing the situation as an "invasion."
In a bid to deal with the large numbers arriving, former prime minister Boris Johnson's government introduced a scheme to deport asylum seekers thousands of miles away to Rwanda, provoking a storm of outrage.
Britain's diplomatic adversaries also jumped on the issue, with Russian representative Nikita Zhukov slamming "London's highly selective approach to the reception of migrants from other mainly African countries".
China's representative Qi Lin meanwhile urged Britain to "put an end to the violation of rights migrants and refugees."