Mr Morrison said the government's Operation Sovereign Borders program was "maintaining significant momentum", but the pre-monsoon season is challenging.
He said last November there were 2630 asylum seekers on 43 boats and so far this month there had been four boats carrying fewer than 200 people.
"We remain though very much on watch and stand at the ready because ... this is typically a period of high intensity and we have no doubt that smugglers will seek to try things on as we move into that last phase before the monsoon," Mr Morrison told reporters in Sydney on Friday.
Mr Morrison declined to comment on Australia's border protection activities with Indonesia, given the diplomatic flare-up this week over claims Australian spies tapped the mobile phones of Indonesian President Susilo Bambang Yudhoyono, his wife's and some of his closest confidants in 2009.
"There are serious issues that need to be worked through in this area and further comment from me would not assist our national interest," he said.
"I do not intend to provide any further comment on those relationship issues.
"Those matters are being directly addressed by the prime minister with the president."
Operation Sovereign Borders Commander, Lieutenant General Angus Campbell also declined to comment, saying it was a government-to-government issue.