"A much faster turnaround on asylum seekers", Kelly told National Public Radio during a controversial interview in which he argued that undocumented migrants would not be able to easily assimilate into American society because "they don't have skills".
The two leaders had made a decision to focus on broad issues to leave more room for negotiations with the other 17 euro members, Macron said - a scenario that leaves scope for the plans to be watered down.
A major crisis occurred in Germany's ruling coalition during the past weekend over migrant policy, control over the country's borders and expulsion of illegal immigrants.
Seehofer's Christian Social Union party had raised the prospect of the minister taking such action in defiance of the chancellor, which has escalated the issue into a threat to her government. He agreed to give the chancellor until after next week's European summit to agree on a European solution that will slow entry of refugees into Germany.
Though Merkel had been lukewarm on Macron's idea of a European budget, in a declaration adopted by both leaders following the meeting they said they had agreed upon a proposal to establish one aimed at "competitiveness and convergence".
Striking a conciliatory tone in a guest column in the Frankfurter Allgemeine paper, Seehofer said the cohesion of Europe and Germany was at stake.
German Chancellor Angela Merkel is given 2-week deadline by her coalition partners, the Christian Social Union, over stricter migration and asylum rules.
Seehofer's demand to turn back migrants has set off a dispute with Merkel, who is against Germany taking unilateral action.
The number of applications for asylum in Germany dropped by 70 percent in 2017 compared to the previous year but Germany remains the main target for asylum seekers in the EU.
Trump on Monday claimed that "crime in Germany is way up".
Seibert declined to elaborate ahead of the meeting, which will be preceded by statements from the leaders.
For Merkel, in power for over 12 years, the stakes could not be higher as she leads an uneasy coalition government with a narrow majority that took half a year to cobble together.
The leaders met to prepare for a summit of European Union leaders on June 28-29, with Mr Macron keen to push through wide-ranging reforms to strengthen the euro zone and insulate the single currency union from future crises, while Dr Merkel has been more cautious.
Seibert said such agreements could involve countries that are most strongly affected by migrant movements.
German chancellor faces challenge that could bring down her government from Bavarian Interior Minister Horst Seehofer over refugees.
European capitals from Rome to Budapest have long called for such centres but concerns that processing people outside EU borders could violate the law have stalled progress. But because immigration is a very divisive topic in the union, Merkel will struggle to find a deal with the other member countries in so little time.
It is unclear if Trump will support legislation that allows undocumented families to remain united if the bill does not also include funding to build his oft-promised border wall, which he initially said Mexico would pay for.
The CSU exists only in Bavaria, while Merkel's less conservative CDU is in Germany's other 15 states.
The AfD, which is expected to poach votes from the CSU in October, accused Seehofer of electioneering.