In \(\mathbb{R}^3\) the family \(\Gamma\) of straight lines \(\xi_1 = x_1 + (\xi_3 - x_3) \cos \alpha\), \(\xi_2 = x_2 + (\xi_3 - x_3) \sin \alpha\), \(0 \leq \alpha \leq 2 \pi\), passing through the point \(x = (x_1, x_2, x_3)\), and the equation \[ \int_\Gamma u(\xi)d \ell + \int_{\mathbb{R}^3} \theta (k) \rho (\alpha, x, \xi) u(\xi)d \xi = v(x, \alpha) \] are considered, where \(d \ell\) is the length element of a straight line, \(\rho (\alpha, x, \xi)\) is a given weight function, \(\theta (k)\) is the characteristic function of the domain \(K = \{(\xi, x) : (\xi_3 - x_3)^2 - (\xi_1 - x_1)^2 - (\xi_2 - x_2)^2 \geq 0\}\). Some sufficient conditions of uniqueness of the solution are established.