Lwin pointed to the number of Bangladeshis on board a migrant boat that landed in May as proof that the influx of "boat people" was a regional problem linked to human trafficking.
"This incident ... has shown to the region as well as the international community this is not the root cause," he said.
The boat he referred to was intercepted by Myanmar's navy last month. Myanmar has said 200 of the 208 people aboard were economic migrants from Bangladesh. But a Reuters investigation found that 150 to 200 Rohingya had also been aboard that boat, but were spirited away by people smugglers in the week before the navy brought it to shore.
Tareque Muhammad, the deputy chief of mission at the Bangladesh embassy in Yangon, told Reuters that only 150 people from that boat had been identified and documented as Bangladeshis.
The bringing to shore of the migrants comes a day after the U.S. called on Myanmar to give full rights to the minority to help end the exodus.
U.S. President Barack Obama said this week that Myanmar needed to end discrimination against the Rohingya if it was to succeed in its transition to a democracy, as Washington increased pressure on the country to tackle what it sees as one of the root causes of a wave of migration that the region has struggled to cope with.
The crisis blew up last month after a Thai crackdown on trafficking camps along its border with Malaysia made it too risky for people smugglers to land their human cargo. Smugglers abandoned boats full of migrants at sea. Images of desperate people crammed aboard overloaded boats with little food or water focused international attention on the unfolding disaster.
Some 4,000 migrants from Bangladesh and Myanmar have landed in Indonesia, Malaysia, Thailand and Myanmar in the past month. Indonesia said on Thursday it was continuing search and rescue operations to find migrant boats.
The United Nations estimates around 2,000 migrants may still be adrift. Indonesia repatriates economic migrants from Bangladesh, but handling Rohingya migrants is more complex, said Andi Rachmianto, the international security and disarmament director at the foreign ministry.
"We need to differentiate between Rohingya migrants and migrants from Bangladesh because their motivations are different," Rachmianto said, noting that most of the Bangladeshis were economic migrants. "So resolving this is relatively easy compared with resolving the case of our Rohingya brothers."