Washington (CNN) A little more than a week after their frosty White House meeting, President Donald Trump and his German counterpart, Angela Merkel, spoke by phone Monday, ostensibly for the US leader to congratulate the chancellor on her party's victory in a tiny German province over the weeken d.

But the call, according to US officials, was also designed to smooth over any lingering unpleasantness from the March 17 meeting, during which Trump focused intently on Germany's defense spending, even when Merkel sought to move on to other topics.

The technique of using a political victory in a local election to flatter an important foreign leader is new for Trump, but not an entire surprise for a president still basking in his own political victory. Trump still recounts his election night win in public remarks, and foreign leaders hoping to foster close ties to the US President have made a point of praising his unlikely campaign during joint appearances.

Trump adopted that approach for himself Monday, phoning both Merkel and Indian Prime Minister Narendra Modi to congratulate them on their parties' state-level wins.

One German government official suggested the call with Merkel amounted to Trump "making an effort to be nice" after their first face-to-face meeting a week and a half ago.

In their conversation, Trump and Merkel discussed the contentious sit-down, though US officials said Trump did not apologize during the phone call for his aggressive stance on NATO, which rankled some German officials. But he did seek to strike a more conciliatory tone with Merkel, with whom he hopes to work together on a range of subjects -- from trade to Syria and Ukraine.

Last week's meeting commenced on an awkward note when Trump appeared to refuse to shake Merkel's hand during an Oval Office photo-op. The body language came to symbolize the vast gulf between the two leaders, which was exacerbated by memories of Trump's campaign trail criticism of Merkel's stance on refugees.

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In their meeting, Trump returned repeatedly to the defense spending issue, according to people familiar with the two leaders' conversation.

He did not, as a British newspaper reported over the weekend, present a physical invoice to Merkel for unpaid funds. But he did maintain, in what one official described as an aggressive tone, that Germany owed vast sums to NATO and the US.

Merkel told Trump during their talks that Germany had committed to ramping up military spending but avoided engaging him on the issue of back payments. But even with those assurances, Trump was intent on driving his point home, even when the German chancellor attempted to redirect their conversation toward other topics.

A person who spoke with Merkel afterward said the German chancellor -- who isn't known for outward displays of emotion -- did not appear fazed by the session.

A separate German government official described the face-to-face meeting as "fine" and "productive," without the level of awkwardness that some read into the leaders' body language.

The Germans "heard the right messages" on US commitment to NATO and insistence on territorial integrity in Ukraine, the official said, which were the topics Merkel was most intent to discuss.

But some members of the German delegation did privately wonder what level of cooperation could exist between the two leaders given Trump's single-minded focus on the NATO matter.

After Merkel departed the White House, Trump attempted to downplay any suggestions the meeting went poorly. But even then, he inserted a jab at Germany's defense budget.

"Despite what you have heard from the FAKE NEWS, I had a GREAT meeting with German Chancellor Angela Merkel," Trump wrote on Twitter while he was at his Florida estate Mar-a-Lago. "Nevertheless, Germany owes vast sums of money to NATO & the United States must be paid more for the powerful, and very expensive, defense it provides to Germany!"

Despite what you have heard from the FAKE NEWS, I had a GREAT meeting with German Chancellor Angela Merkel. Nevertheless, Germany owes..... — Donald J. Trump (@realDonaldTrump) March 18, 2017

...vast sums of money to NATO & the United States must be paid more for the powerful, and very expensive, defense it provides to Germany! — Donald J. Trump (@realDonaldTrump) March 18, 2017

That message added to the anxiety of some German officials, who were unnerved by the combative public stance toward an important US ally. Some US officials also expressed private concern that Trump risked alienating Merkel, who is Europe's longest-serving, most politically assured leader and has expressed a desire to maintain a close working relationship with Washington.

Ivanka Trump, the President's daughter, has herself sought to foster a connection with Merkel in a bid to maintain Berlin-Washington ties. At Merkel's request, the first daughter arranged a meeting between US and German CEOs as part of the Chancellor's visit; the session was a highlight of the day, according to German officials. Ivanka Trump will visit Berlin for a women's empowerment summit in April.

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Monday's phone call was added to Trump's schedule after Merkel's Christian Democrats won a regional election in a tiny western state over the weekend. In an official readout of the phone conversation, the White House said Trump spoke with Merkel "to congratulate her on the outcome of the Saarland state election on March 26."

But the statement also added that the two leaders "used the occasion to reflect on the Chancellor's March 17 visit to the White House."

Trump employed a less aggressive tone and did not repeat his claim that Germany owed the US money, said US officials familiar with the call. He instead used the local elections as a way to flatter Merkel.

Sunday's vote in Saarland state -- Germany's smallest -- isn't expected to have a major impact on the balance of power in Germany, and the Christian Democrats have held power in the area for the better part of two decades.

But the election was seen as a bellwether for a series of upcoming votes in Germany, ending in the federal elections on September 24.

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Merkel's party performed better than expected. The center-right Christian Democrats won 40.7% of Sunday's vote, a solid 5.5% increase over four years ago and a convincing win over the center-left Social Democrat Party, which only took 29.6%, according to CNN affiliate ARD.

The Saarland elections were widely viewed as a test for the SPD's new leader, former EU Parliament President Martin Schulz, whose criticism of Trump's policies appeared to be playing well with voters.

It's rare for a US president to call foreign leaders to congratulate them on their parties' political successes, particularly in local elections when the leader is not herself on the ballot. Indeed, the White House typically take pains to avoid seeming to interfere in foreign political contests.

On Tuesday, however, the White House also said Trump had phoned India's prime minister to "congratulate him on the outcome of India's recent state-level elections."

Modi's Bharatiya Janata Party won a landslide victory earlier this month in Uttar Pradesh, India's most populous state. That election was regarded as a direct win for Modi himself, who campaigned in the district for his party and will come up for a second term in 2019.