Greer was speaking in Kuala Lumpur at the start of a meeting with economic ministers from the 10-member Association of Southeast Asian Nations, amid concerns within the export-reliant bloc over the impact of US tariffs on their economies.
Tariff rates have been set at 19 per cent and 20 per cent for most of the region.
Laos and Myanmar have been hit with a 40 per cent rate, while Singapore has a 10 per cent tariff.
Greer said talks with respective countries on the levies had been progressing well, resulting in some deals being announced while others will be finalised "in the coming months or even weeks, for some".
The United States has said it had reached agreements with Indonesia and Vietnam on tariffs, though the countries say they are still finalising terms.
Vietnam, the world's sixth-largest exporter to the United States, risks losing $US25 billion ($A38 billion) annually as a result of the 20 per cent tariff imposed on its goods, which would make it the worst-hit economy in the region, according to estimates released by the United Nations Development Programme.
In a joint statement dated on Tuesday, ASEAN economic ministers noted "adverse impact and uncertainty" arising from the tariff landscape and warned of slower regional trade performance in the second half of 2025, due to the front-loading of exports before the tariffs' imposition in the earlier part of the year.
The ministers also expressed concern over rising protectionism and unilateral trade measures, which they say "pose significant risks to the multilateral trading system and the stability of global supply chains".
In his remarks, Greer said the United States welcomed trade with ASEAN but it must be "balanced and reciprocal".
"We believe that there are many areas where our interests align, and we can work together to achieve shared goals of bringing reciprocity and balance to the global trading system," he said.
Wednesday marked Greer's first meeting with the ASEAN bloc, whose members have largely engaged in separate negotiations with the United States on the issue of tariffs.
But the grouping might be driven to take a more unified position amid risks of steeper sectoral tariffs on industries such as semiconductors, a significant contributor to economies such as Thailand, Malaysia, and Vietnam.
US President Donald Trump said in August he would set a tariff of about 100 per cent on semiconductors, but it would not apply to companies that are manufacturing in the United States or have committed to do so.
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