Rumors started swirling last week about a breakdown in trade talks between the U.S. and China after President Donald Trump said he hadn’t agreed to any tariff relief as part of a proposed phase one agreement.

Experts inside and outside the U.S. government warn that the phase one trade pact could fall apart. U.S. officials said a lot of work remained to be done when Trump announced the outlines of an interim deal last month.

Beijing has since pushed back on U.S. demands for big agricultural purchases,...