  Charmed tetraquarks $T_{cc}=(cc\bar{u}\bar{d})$ and
$T_{cs}=(cs\bar{u}\bar{d})$ are studied through the S-wave meson-meson
interactions, $D$-$D$, $\bar{K}$-$D$, $D$-$D^{*}$ and $\bar{K}$-$D^{*}$, on the
basis of the (2+1)-flavor lattice QCD simulations with the pion mass $m_{\pi}
\simeq $410, 570 and 700 MeV. For the charm quark, the relativistic heavy quark
action is employed to treat its dynamics on the lattice. Using the HAL QCD
method, we extract the S-wave potentials in lattice QCD simulations, from which
the meson-meson scattering phase shifts are calculated. The phase shifts in the
isospin triplet ($I$=1) channels indicate repulsive interactions, while those
in the $I=0$ channels suggest attraction, growing as $m_{\pi}$ decreases. This
is particularly prominent in the $T_{cc} (J^P=1^+,I=0)$ channel, though neither
bound state nor resonance are found in the range $m_{\pi} =410-700$ MeV. We
make a qualitative comparison of our results with the phenomenological diquark
picture.
